detrended fluctuation analysis of intertrade durations abstract the intraday pattern long memory and multifractal nature of the intertrade durations which are defined as the waiting times between two consecutive transactions are investigated based upon the limit order book data and order flows of 23 liquid chinese stocks listed on the shenzhen stock exchange in 2003 an inverse u shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed based on a detrended fluctuation analysis we find a crossover of power law scaling behaviors for small box sizes trade numbers in boxes and large box sizes and strong evidence in favor of long memory in both regimes in addition the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small duration regime the intraday pattern has little influence on the long memory and multifractality

lacunarity and multifractal analysis of the large dla mass distribution abstract we show the methodology used to analyze fractal and mass multifractal properties of very large diffusion limited aggregation dla clusters with a maximum of 10 9 particles for 2d aggregates and 10 8 particles for 3d clusters to support our main result the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects in order to estimate lacunarity measures for large dla clusters we develop a variant of the gliding box algorithm which reduces the computer time needed to obtain experimental results we show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters lacunarity analysis shows provided we study small clusters mass distributions data which might be interpreted as two different values of fractal dimensions while the cluster grows however this effect tends to vanish when the cluster size increases further in such a way that monofractality is achieved the outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior vicsek et al 1990 13 detected for dla clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena since the scaling behavior of our dla clusters space corresponds to monofractal objects being this situation remarkably noticeable in the limit of very large clusters

multifractal analysis of ssec in chinese stock market a different empirical result from heng seng index abstract in this paper high frequency per 5 min data of shanghai stock exchange composite index ssec from january 1999 to july 2001 is analyzed by multifractal we find that the correlation of the parameters of the multifractal spectra with the variation of daily return z in ssec is noticeably different from that in previous studies of heng seng index in hong kong stock market sun et al phys a 291 2001 553 562 sun et al phys a 301 2001 473 482 so we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index then we construct a new measurement of market risk based on multifractal spectra and test its ability of predicting index fluctuations with a more thorough method than that in sun et al phys a 301 2001 473 482

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

moment stability of nonlinear stochastic systems with time delays based on cal h representation technique in this note moment stability of nonlinear stochastic systems with time delays is investigated based on a kind of kronecker algebra and the h representation technique we obtain the second order moment equations of nonlinear stochastic systems with time delays by the comparison principle and the established moment equations we get the comparative systems of the nonlinear stochastic systems with time delays then we establish moment stability theorems for the systems with the stability properties of the comparative systems finally an example is presented to illustrate the efficiency of our results

multiplier phenomenology in random multiplicative cascade processes we demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artifact of the observation procedure taking the latter into account all reported properties of both unconditioned and conditioned multiplier distributions can be reproduced by cascade models with uncorrelated random weights if their bivariate splitting function is nonenergy conserving for the ensuremath alpha model we show that the simulated multiplier distributions converge to a limiting form which is very close to the experimentally observed one if random translations of the observation window are accounted for also the subtle effects found in conditioned multiplier distributions are precisely reproduced

multifractal behavior of the korean stock market index kospi abstract we investigate multifractality in the korean stock market index kospi the generalized qth order height height correlation function shows multiscaling properties there are two scaling regimes with a crossover time around t c 40 min we consider the original data sets and the modified data sets obtained by removing the daily jumps which occur due to the difference between the closing index and the opening index to clarify the origin of the multifractality we also smooth the data through convolution with a gaussian function after convolution we observe that the multifractality disappears in the short time scaling regime t t c but remains in the long time scaling regime t t c regardless of whether or not the daily jumps are removed we suggest that multifractality in the short time scaling regime is caused by the local fluctuations of the stock index but the multifractality in the long time scaling regime appears to be due to the intrinsic trading properties such as herding behavior information outside the market the long memory of the volatility and the nonlinear dynamics of the stock market

nonclassical eigenvalue asymptotics abstract the leading asymptotics for the growth of the number of eigenvalues of the two dimensional dirichlet laplacian in the regions x y x y 1 and for x y all of which are non weyl because of infinite phase space volumes are computed along the way a general inequality on quantum partition functions computed in a kind of born oppenheimer approximation is proved

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

on the spectrum of the dirichlet laplacian for horn shaped regions in rn with infinite volume abstract an inequality for trace et d is proven where d is the dirichlet laplacian for horn shaped regions d in rn the results of rozenbljum and simon for the leading asymptotics for the growth of the number of eigenvalues of the two dimensional dirichlet laplacian in the regions x y x y 1 0 are easily recovered an example of a horn shaped region in r2 where that asymptotics is exponential is given

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

the almost sure asymptotic stability and p th moment asymptotic stability of nonlinear stochastic differential systems with polynomial growth this note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems sdss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such sdss we also provide the range of the order p a numerical example is provided to illustrate the effectiveness and the benefits of the proposed result

nonclassical eigenvalue asymptotics for operators of schrodinger type on considere des operateurs de la forme a v x sur r n ou la metrique ij x 0 et le potentiel v x 0 on etudie la fonction de denombrement des valeurs propres par un calcul pseudo differentiel avec des symboles a valeur d operateurs

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

a simple separable hamiltonian having bound states in the continuum the author discusses a simple separable two freedom hamiltonian h describing the motion of a point particle in a plane region v 0 between two infinite parallel hard walls v infinity and with a rectangular finite potential well v v0 the quantal spectrum of h is discrete below the continuum limit ionisation energy different from the classical escape energy e 0 by the zero point energy of the transverse motion and has infinitely many bound states embedded in the continuum the author shows that this spectrum is fragile against perturbations of h if the hard walls are made diverging the bound states in the continuum disappear while if they are converging the continuum disappears and the spectrum is pure point

nonlinear complexity of random visibility graph and lempel ziv on multitype range intensity interacting financial dynamics abstract in an attempt to investigate the nonlinear complex evolution of financial dynamics a new financial price model the multitype range intensity contact mric financial model is developed based on the multitype range intensity interacting contact system in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading two new random visibility graph vg based analyses and lempel ziv complexity lzc are applied to study the complex behaviors of return time series and the corresponding random sorted series the vg method is the complex network theory and the lzc is a non parametric measure of complexity reflecting the rate of new pattern generation of a series in this work the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further the numerical empirical study shows the similar complexity behaviors between the model and the real markets the research confirms that the financial model is reasonable to some extent

a flexible terminal approach to stochastic stability and stabilization of continuous time semi markovian jump systems with time varying delay abstract this paper addresses the stochastic stability and stabilization problems for a class of semi markovian jump systems smjss with time varying delay where the time varying delay t is assumed to satisfy 1 t 2 based on the flexible terminal approach the time varying delay t is first transformed such that 1 t t 2 t by utilizing a novel semi markovian lyapunov krasoviskii functional smlkf and an improved reciprocally convex inequality rci sufficient conditions are established to guarantee a feasible solution two illustrated examples are shown the effectiveness of the main results

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series

visibility graph network analysis of gold price time series abstract mapping time series into a visibility graph network the characteristics of the gold price time series and return temporal series and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory the network degree distribution characters which change from power law to exponent law when the series was shuffled from original sequence and the average path length characters which change from l ln n into ln l ln n as the sequence was shuffled demonstrate that price series and return series are both long rang dependent fractal series the relations of hurst exponent to the power law exponent of degree distribution demonstrate that the logarithmic price series is a fractal brownian series and the logarithmic return series is a fractal gaussian series power law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series the power law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network the hierarchy character in light of the correspondence of graph to price fluctuation means that gold price fluctuation is a hierarchy structure which appears to be in agreement with elliot s experiential wave theory on stock price fluctuation and the local rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent short term factors such as short term speculation

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

dirichlet neumann bracketing for horn shaped regions we use dirichlet neumann bracketing to obtain sharp upper and lower bounds for the spectral counting function of the dirichlet laplacian for a horn shaped region in rm the first and second term and an estimate for the remainder in the asymptotic expansion of the spectral counting function are obtained for a region in r2 given by x1 x2 x1er x2e x1 x2 1 2 12 212

fault tolerant control for fuzzy switched singular systems with persistent dwell time subject to actuator fault abstract this paper investigates the problem of fault tolerant state feedback fuzzy control for discrete time nonlinear switched singular systems subject to the actuator fault the typical takagi sugeno model is utilized to process the nonlinearity of the systems for the purpose of describing the intermittent occurrence of fast and slow switching among subsystems a switching signal complying with persistent dwell time switching regularity is introduced for the first time into the analysis of nonlinear switched singular systems the primary objective is focused on constructing a fault tolerant controller which can ensure that the closed loop system is exponentially admissible with a prescribed l 2 gain performance in the presence of actuator fault by using mode dependent lyapunov function and employing an improved matrix decoupling method sufficient conditions with less conservatism for the existence of the desired controller are established and the explicit form of the controller gains is presented for explaining the effectiveness of the proposed method two illustrative examples are given finally

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

improved shell model of turbulence we introduce a shell model of turbulence that exhibits improved properties in comparison to the standard and very popular gledzer ohkitani and yamada goy model the nonlinear coupling is chosen to minimize correlations between different shells in particular the second order correlation function is diagonal in the shell index and the third order correlation exists only between three consecutive shells spurious oscillations in the scaling regime which are an annoying feature of the goy model are eliminated by our choice of nonlinear coupling we demonstrate that the model exhibits multiscaling similar to the goy model the scaling exponents are shown to be independent of the viscous mechanism as is expected for navier stokes turbulence and other shell models these properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics

mean square stability and almost sure exponential stability of two step maruyama methods of stochastic delay hopfield neural networks abstract in this paper the two step maruyama methods of stochastic delay hopfield neural networks are studied we have found that under what choices of step size the two step maruyama methods of stochastic delay hopfield networks maintain the stability of exact solutions the mean square stability of two step maruyama methods of stochastic delay hopfield neural networks is investigated under suitable conditions also the almost sure exponential stability of two step maruyama methods of stochastic delay hopfield networks is proved using the semi martingale convergence theorem further the comparisons of stability conditions to the previous results in liu and zhu 2015 rathinasamy 2012 and ronghua et al 2010 are given numerical experiments are provided to illustrate our theoretical results

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

sampled data h exponential synchronization for delayed semi markov jump cdns a looped functional approach abstract this paper investigates the h exponential synchronization problem of delayed semi markov jump complex dynamical networks by utilizing the sampled data control scheme through introducing a semi markov jump model where the transition rate is related to the sojourn time the addressed issue is therefore more general by constructing a suitable lyapunov krasovskii functional with a looped functional and adopting an advanced inequality method sufficient conditions for the h exponential synchronization of delayed semi markov jump complex dynamical networks are presented a numerical example is finally employed to confirm the validity of the proposed method

delay dependent robust stability of uncertain neutral type it stochastic systems with markovian jumping parameters this paper investigates the problem of mean square exponential stability for uncertain neutral stochastic systems with time delays and markovian jumping parameters based on the new results on expectations of stochastic cross terms containing the it o integral by song et al 2013 a new lyapunov krasovskii function is established and then an improved mean square exponential stability criterion is derived the derived results extend the conclusions recently presented in song et al 2013 in fact the system discussed in song et al 2013 is a special case of ours finally two examples are provided to demonstrate the effectiveness of the proposed results

negative fractal dimensions and multifractals abstract a new notion of fractal dimension is defined when it is positive it effectively falls back on known definitions but its motivating virtue is that it can take negative values which measure usefully the degree of emptiness of empty sets the main use concerns random multifractals for which f

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

on the properties of random multiplicative measures with the multipliers exponentially distributed under the formalism of annealed averaging of the partition function a type of random multifractal measures with the multipliers exponentially distributed is investigated in detail branching emerges in the curve of generalized dimensions and negative values of generalized dimensions arise three equivalent methods of classification of the random multifractal measures are proposed which is based on i the properties of the curves of generalized dimensions ii the solution properties of equation q 0 and iii the relative position of the curve f and the diagonal f in the first quadrant these classes of measures correspond to 0 1 0 1 1 and 0 1 0 respectively phase diagram is introduced to illustrate the diverse performance of the random measures that is multiplicatively generated

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

generalizations of the classical weyl and colin de verdiere s formulas and the orbit method the classical weyl formula expresses the leading term of the asymptotics of the counting function n h of the spectrum of a self adjoint operator h in an invariant form one can hear the volume of the subset of the cotangent bundle where the symbol of the operator h is less than in particular it is applicable to schrodinger operators with electric potentials growing at infinity the weyl formula is formulated in an invariant form however it gives for magnetic schrodinger operators with magnetic tensors growing at infinity for these operators colin de verdiere s formula is known but the form of the latter is not invariant in this article we suggest an invariant generalization of both weyl s and colin de verdiere s formulas for wide classes of schrodinger operators with polynomial electric and magnetic fields the construction is based on the orbit method due to kirillov and it allows one to hear the geometry of coadjoint orbits

reachable set estimation for markov jump lpv systems with time delays abstract this paper investigates the reachable set estimation problem for discrete time markov jump lpv systems with time varying delays and bounded disturbance the main consideration is that under zero initial conditions how to obtain a bound set as small as possible that includes system states based on this by applying a novel summation inequality integrated with the reciprocally convex approach under the framework of the lyapunov functional method the delay dependent conditions are provided to guarantee the presence of an ellipsoid that bounds the system state in the existence of bounded disturbances some derived conditions expressed by linear matrix inequalities can be solved via utilizing different computational tools and the minimum possible ellipsoidal bound can also be determined additionally the obtained results are extensively used in the case with partially known transition probability and some conditions with more universality are derived finally a numerical example is given to illustrate the effectiveness of the results

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

the effects of common risk factors on stock returns a detrended cross correlation analysis abstract in this paper we investigate the cross correlations between fama and french three factors and the return of american industries on the basis of cross correlation statistic test and multifractal detrended cross correlation analysis mf dcca qualitatively we find that the return series of fama and french three factors and american industries were overall significantly cross correlated based on the analysis of a statistic quantitatively we find that the cross correlations between three factors and the return of american industries were strongly multifractal and applying mf dcca we also investigate the cross correlation of industry returns and residuals we find that there exists multifractality of industry returns and residuals the result of correlation coefficients we can verify that there exist other factors which influence the industry returns except fama three factors

interval stability and stabilization of linear stochastic systems this technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time invariant systems first the notion of beta alpha stability of stochastic systems is defined and some relationships among the beta alpha stability the decay rate of system state response and the second order moment lyapunov exponent are revealed we then address the beta alpha stabilization problem and give a sufficient condition via a linear matrix inequality approach

on the wavelet transformation of fractal objects the wavelet transformation is briefly presented it is shown how the analysis of the local scaling behavior of fractals can be transformed into the investigation of the scaling behavior of analytic functions over the half plane near the boundary of its domain of analyticity as an example a weierstrass like fractal function is considered for which the wavelet transform is related to a jacobi theta function some of the scalings of this theta function are analyzed and give some information about the scaling behavior of this fractal

some new criteria on p th moment stability of stochastic functional differential equations with markovian switching this note gives some new razumikhin type theorems on th moment stability of stochastic functional differential equations with markovian switching sfdewms by using auxiliary ordinary differential equation the main results of this note allow the diffusion operator associated with the underlying sfdewms of the lyapunov function along a solution of the system to be not always negative an example is provided to illustrate the effectiveness of the proposed results

predictability of multifractal analysis of hang seng stock index in hong kong in this paper the daily hang seng index in hong kong stock market is studied by multifractal analysis the main parameter of multifractal spectra used is f which can be used to characterize the ratio of number of highest index moments to that of lowest ones the dependence of today s gain probability g and the day s index increase probability n with f of the previous 3 days are studied it is found that g and n can reach 70 80 at the large positive f region and can be very close to 20 at the big negative f region the predictability decreases with the increasing number of the previous days

multifractal analysis of hang seng index in hong kong stock market abstract in this paper the daily hang seng index in hong kong stock market is analyzed by multifractal the correlation of the parameters of the multifractal spectra with the variation of close return z is studied statistically it is found that the amount of the variation of return is correlated with the amount of of that day the increase or decrease of the return is related to the positive or negative value of f the gain probability and the increasing day s probability can be higher than 70 at the larger f region and be lower than 20 at the more negative region

nonlinear structure analysis of carbon and energy markets with mfdcca based on maximum overlap wavelet transform abstract this paper investigates the nonlinear structure between carbon and energy markets by employing the maximum overlap wavelet transform modwt as well as the multifractal detrended cross correlation analysis based on maximum overlap wavelet transform mfdcca modwt based on the modwt multiresolution analysis and the statistic q c c m significance relatively significant cross correlations are obtained between carbon and energy future markets either on different time scales or on the whole the result of the granger causality test indicates bidirectional granger causality between carbon and electricity future markets although the granger causality relationship between the carbon and oil price is not evident the existence of multifractality for the returns between carbon and energy markets is proven with the mfdcca modwt algorithm in addition results of investigating the origin of multifractality demonstrate that both long range correlations and fat tailed distributions play important roles in the contributions of multifractality

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized h representation abstract the problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper firstly we define the generalized h representation which is very helpful to transform stochastic systems into deterministic systems then the problems of pth moment interval stability the decay rate of state response and the estimation of pth moment lyapunov exponent are proposed with the help of the model transformation method furthermore the criteria for pth moment interval stabilization of the linear stochastic systems are addressed some necessary numerical examples are also provided to show the effectiveness of the addressed method

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

spectral asymptotics for the schrodinger operator with potential which steadies at infinity we consider the discrete spectrum of the selfadjoint schrodinger operatora h h 2 v defined inl2 m with potentialv which steadies at infinity i e v x g x f 1 o 1 as x for 0 and some homogeneous functionsg andf of order zero let h 0 be the total multiplicity of the eigenvalues ofa h smaller thanm m being the minimum value ofg over the unit spheresm 1 hence m coincides with the lower bound of the essential spectrum ofa h we study the asymptotic behaviour of 1 as 0 or of h ash 0 the number 0 being fixed we find that these asymptotics depend essentially on the structure of the submanifold ofsm 1 where the functiong takes the valuem and generically are nonclassical i e even as a first approximation 2 m h differs from the volume of the set x 2m h2 2 v x m

on the spectral counting function for the dirichlet laplacian abstract we obtain upper and lower bounds for the spectral counting function associated to the dirichlet laplacian for an open set d in euclidean space satisfying a geometric and a potential theoretic condition

eigenvalue asymptotics and exponential decay of eigenfunctions for schrodinger operators with magnetic fields we consider the schr6dinger operator with magnetic field h va x 2 v x in rj assuming that v 0 and icurl a i v 1 is locally in certain reverse holder class we study the eigenvalue asymptotics and exponential decay of eigenfunctions introduction consider the schrodinger operator with magnetic field 0 1 h h a v jv a x v x inlr n 3 where i 1 v rn r is the electric scalar potential and a rn rn is the magnetic vector potential under some natural conditions on a and v h admits a self adjoint realization which is still denoted by h in l2 ir1n in this paper we shall study its eigenvalue asymptotics and exponential decay of its eigenfunctions let n a h denote the number of eigenvalues counting multiplicity of h smaller than a or the dimension of the spectral projection for h corresponding to x a in the case a x 0 the following phase space volume estimate due to cwickel lieb rosenbljum sil theorem 9 3 p 95 is classical 0 2 n a a v cnl i x e r n x r n 1h12 v x l where cn is a constant depending on n on the other hand there exist some simple degenerate potentials v x i e potentials which do not tend to infinity in all direction as lxi oo e g v x v xi x2 xn x2x n xn for which the right hand side of 0 2 is infinite and nevertheless a v x has a discrete spectrum furthermore in the case where a x 0 and v x 0 the phase space volume of the set where the symbol of h is less than a n i x e nr x r n e ijaj x l2 l j 1 received by the editors may 19 1995 1991 mathematics subject classification primary 35p20 35j10

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

fix point multiplier distributions in discrete turbulent cascade models abstract one point time series measurements limit the observation of three dimensional fully developed turbulence to one dimension for one dimensional models like multiplicative branching processes this implies that the energy flux from large to small scales is not conserved locally this then renders the random weights used in the cascade curdling to be different from the multipliers obtained from a backward averaging procedure the resulting multiplier distributions become solutions of a fix point problem with a further restoration of homogeneity all observed correlations between multipliers in the energy dissipation field can be understood in terms of simple scale invariant multiplicative branching processes

inverse statistics and multifractality of exit distances in 3d fully developed turbulence abstract the inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions 1 2 3 4 using taylor s frozen field hypothesis we investigate the statistical properties of the exit distances of empirical 3d fully developed turbulence we find that the probability density functions of exit distances at different velocity thresholds v can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold we show that the inverse structure functions exhibit clear extended self similarity ess the ess exponents p 2 for small p p 3 5 are well described by p 2 p 2 which derives from the observed approximate universality of the distributions of the exit distances for different velocity thresholds v the data is not sufficient to reject the hypothesis that monofractal ess is sufficient to explain the data in contrast a measure taking into account the dependence between successive exit distances at a given velocity threshold exhibits clear multifractality with negative dimensions suggesting the existence of a non trivial dependence in the time series of exit times

auto correlated behavior of wti crude oil volatilities a multiscale perspective abstract in this paper we investigate the long range auto correlated behavior of wti crude oil volatility series employing multifractal detrended fluctuation analysis our findings show that the for small time scales the auto correlations of volatilities were multifractal while for large time scales the auto correlations were nearly monofractal based on multiscale analysis we also investigate the dynamics of auto correlations for different intervals of time scales and find that several shocks could make significant effects on the auto correlated behaviors for small time scales analyzing the dynamics of multifractality degrees of auto correlations for small time scales we find that the stronger auto correlations were always related to the lower degrees of multifractality at last we have discussions on the determination factors of price behavior the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long range auto correlations of volatility were always strong for both small time scales and large time scales our results are very important theoretically and practically

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

scaling behavior in ranking mobility of chinese stock market abstract as an aggregate measure of the variations in individuals the analysis of mobility provides a substantial and comprehensive perspective into the complexity of socio economic systems in this paper we introduced the ranking mobility index to measure the ranking variations of the stocks in chinese stock market over time using the daily data of 837 constituent stocks of the shanghai a stock composite index from january 1 2002 to december 31 2012 we examined respectively the dependence of ranking mobility with respect to the absolute return trading volume and turnover ratio on the sampling time interval the scaling property is observed in all three relations the fact of long relaxation times gives evidence of long memory property in the stock ranking orders

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

classical and non classical eigenvalue asymptotics for magnetic schrodinger operators abstract in this paper we consider schrodinger operators with magnetic fields and study which of the magnetic field and the scalar potential contributes to the leading term of the asymptotic distribution of eigenvalues by studying the asymptotic behavior of the trace of the heat kernels we see that if the norm of the magnetic field diverges at infinity faster than the scalar potential only the magnetic field contributes to the leading asymptotic and that only the scalar potential does if the opposite under mild conditions

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

scaling self similarity and multifractality in fx markets abstract this paper presents an empirical investigation of scaling and multifractal properties of us dollar deutschemark usd dem returns the data set is ten years of 5 min returns the cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space this presents strong evidence that the usd dem returns exhibit power law scaling in the tails to test the multifractal properties of usd dem returns the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns these moments show different slopes for these powers of absolute returns the nonlinearity of the scaling exponent indicates that the returns are multifractal

eigenvalue asymptotics of the neumann laplacian of regions and manifolds with cusps abstract we study the eigenvalue asymptotics of a neumann laplacian n in unbounded regions of r2 with cusps at infinity a typical example is x y r 2 x 1 y x 2 and prove that n e n n e h v e 2 vol where hv is the canonical one dimensional schrodinger operator associated to the problem we establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a dirichlet laplacian d for a class of cusp type regions of infinite volume

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

improved razumikhin and krasovskii stability criteria for time varying stochastic time delay systems the problem of pth moment stability for time varying stochastic time delay systems with markovian switching is investigated in this paper some novel stability criteria are obtained by applying the generalized razumikhin and krasovskii stability approaches both pth moment asymptotic stability and integral input to state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas the established results show that time derivatives of the constructed razumikhin functions and krasovskii functionals are allowed to be indefinite which improve the existing results on this topic by applying the obtained results for stochastic systems we also analyze briefly the stability of time varying deterministic time delay systems finally examples are provided to illustrate the effectiveness of the proposed results

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

generic multifractality in exponentials of long memory processes we find that multifractal scaling is a robust property of a large class of continuous stochastic processes constructed as exponentials of long memory processes the long memory is characterized by a power law kernel with tail exponent ensuremath varphi 1 2 where ensuremath varphi g0 this generalizes previous studies performed only with ensuremath varphi 0 with a truncation at an integral scale by showing that multifractality holds over a remarkably large range of dimensionless scales for ensuremath varphi g0 the intermittency multifractal coefficient can be tuned continuously as a function of the deviation ensuremath varphi from 1 2 and of another parameter ensuremath sigma 2 embodying information on the short range amplitude of the memory kernel the ultraviolet cutoff viscous scale and the variance of the white noise innovations in these processes both a viscous scale and an integral scale naturally appear bracketing the inertial scaling regime we exhibit a surprisingly good collapse of the multifractal spectra ensuremath zeta q on a universal scaling function which enables us to derive high order multifractal exponents from the small order values and also obtain a given multifractal spectrum ensuremath zeta q by different combinations of ensuremath varphi and ensuremath sigma 2

inverse structure functions while the ordinary structure function in turbulence is concerned with the statistical moments of the velocity increment ensuremath delta u measured over a distance r the inverse structure function is related to the distance r where the turbulent velocity exits the interval ensuremath delta u we study inverse structure functions of wind tunnel turbulence which covers a range of reynolds numbers mathrm re ensuremath lambda 400 1100 we test a recently proposed relation between the scaling exponents of the ordinary structure functions and those of the inverse structure functions s roux and m h jensen phys rev e 69 16309 2004 the relatively large range of reynolds numbers in our experiment also enables us to address the scaling with reynolds number that is expected to highlight the intermediate dissipative range while we firmly establish the relative scaling of inverse structure functions our experimental results fail both predictions therefore the question of the significance of inverse structure functions remains open