dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

an intermediate distribution between gaussian and cauchy distributions abstract in this paper we construct an intermediate distribution linking the gaussian and the cauchy distribution we provide the probability density function and the corresponding characteristic function of the intermediate distribution because many kinds of distributions have no moment we introduce weighted moments specifically we consider weighted moments under two types of weighted functions the cut off function and the exponential function through these two types of weighted functions we can obtain weighted moments for almost all distributions we consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory moreover we utilize the intermediate distribution to the problem of the stock market return in quantitative finance

optimal portfolio and consumption decisions for a small investor on a finite horizon a general consumption investment problem is considered for an agent whose actions cannot affect the market prices and who strives to maximize total expected discounted utility of both consumption

superstatistical distributions from a maximum entropy principle we deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information a maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system given certain constraints on the complex system under consideration we apply the theory to three examples the superstatistical quantum mechanical harmonic oscillator the superstatistical classical ideal gas and velocity time series as measured in a turbulent taylor couette flow

superstatistical fluctuations in time series applications to share price dynamics and turbulence we report a general technique to study a given experimental time series with superstatistics crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration the proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions we test the method thoroughly with surrogate data sets then the applicability of the superstatistical approach is illustrated using real experimental data we study two examples velocity time series measured in turbulent taylor couette flows and time series of log returns of the closing prices of some stock market indices

explicit solution of a general consumption investment problem this paper solves a general consumption and investment decision problem in closed form an investor seeks to maximize total expected discounted utility of consumption there are n distinct risky investments modelled by dependent geometric brownian motion processes and one riskless deterministic investment the analysis allows for a general utility function and general rates of return the model and analysis take into consideration the inherent nonnegativity of consumption and consider bankruptcy so this paper generalizes many of the results of lehoczky sethi and shreve lehoczky j s sethi s shreva 1983 optimal consumption and investment policies allowing consumption constraints and bankruptcy math oper res 8 613 636 the value function is determined explicitly as are the optimal consumption and investment policies the analysis is extended to consider more general risky investments under certain conditions the value functions derived for geometric brownian motion are shown to provide upper and lower bounds on the value functions in the more general context

q gaussian diffusion in stock markets we analyze the standard poor s 500 stock market index from the past 22 years the probability density function of price returns exhibits two well distinguished regimes with self similar structure the first one displays strong superdiffusion together with short time correlations and the second one corresponds to weak superdiffusion with weak time correlations both regimes are well described by q gaussian distributions the porous media equation a special case of the tsallis bukman equation is used to derive the governing equation for these regimes and the black scholes diffusion coefficient is explicitly obtained from the governing equation

escort mean values and the characterization of power law decaying probability densities escort mean values or q moments constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws they naturally appear in the study of many complex dynamical systems particularly those obeying nonextensive statistical mechanics a current generalization of the boltzmann gibbs theory they recover standard mean values or moments for q 1 here we discuss the characterization of a non negative probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities provided that all of them converge this opens the door to a natural extension of the well known characterization for the q 1 instance of a distribution in terms of the standard moments provided that all of them have finite values this question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a give

superstatistical fluctuations in time series of leverage returns abstract we analyze to what extent the emergence of fat tailed q gaussian distributions of daily leverage returns of north american industrial companies that survive default and de listing between 2006 and 2012 can be described by superstatistics to this end we compare mean values of the tsallis entropic parameter q obtained by two independent methods i direct fitting of q gaussians to distributions of leverage returns and ii derived from shape parameters of gamma distributions fitted to histograms of inverted realized variances of these returns for a vast majority of companies we observe the striking consistency of average values of q obtained by both methods this finding supports the applicability of superstatistical hypothesis which assumes that q gaussians result from the superposition of locally normal distributions with gamma distributed precision inverted variance

topological data analysis of financial time series landscapes of crashes abstract we explore the evolution of daily returns of four major us stock market indices during the technology crash of 2000 and the financial crisis of 2007 2009 our methodology is based on topological data analysis tda we use persistence homology to detect and quantify topological patterns that appear in multidimensional time series using a sliding window we extract time dependent point cloud data sets to which we associate a topological space we detect transient loops that appear in this space and we measure their persistence this is encoded in real valued functions referred to as a persistence landscapes we quantify the temporal changes in persistence landscapes via their l p norms we test this procedure on multidimensional time series generated by various non linear and non equilibrium models we find that in the vicinity of financial meltdowns the l p norms exhibit strong growth prior to the primary peak which ascends during a crash remarkably the average spectral density at low frequencies of the time series of l p norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03 10 2000 or to the lehman bankruptcy on 09 15 2008 our study suggests that tda provides a new type of econometric analysis which complements the standard statistical measures the method can be used to detect early warning signals of imminent market crashes we believe that this approach can be used beyond the analysis of financial time series presented here

log amplitude statistics for beck cohen superstatistics as a possible generalization of beck cohen superstatistical processes we study non gaussian processes with temporal heterogeneity of local variance to characterize the variance heterogeneity we define log amplitude cumulants and log amplitude autocovariance and derive closed form expressions of the log amplitude cumulants for ensuremath chi 2 inverse ensuremath chi 2 and log normal superstatistical distributions furthermore we show that ensuremath chi 2 and inverse ensuremath chi 2 superstatistics with degree 2 are closely related to an extreme value distribution called the gumbel distribution in these cases the corresponding superstatistical distributions result in the q gaussian distribution with q 5 3 and the bilateral exponential distribution respectively thus our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values in addition as an application of our approach we demonstrated that non gaussian fluctuations observed in a stock index futures market can be well approximated by the ensuremath chi 2 superstatistical distribution with degree 2

a superstatistical model of vehicular traffic flow abstract in the analysis of vehicular traffic flow a myriad of techniques have been implemented in this study superstatistics is used in modeling the traffic flow on a highway segment traffic variables such as vehicular speeds volume and headway were collected for three days for the superstatistical approach at least two distinct time scales must exist so that a superposition of nonequilibrium systems assumption could hold when the slow dynamics of the vehicle speeds exhibit a gaussian distribution in between the fluctuations of the system at large one speaks of a relaxation to a local equilibrium these gaussian distributions are found with corresponding standard deviations 1 this translates into a series of fluctuating beta values hence the statistics of statistics superstatistics the traffic flow model has generated an inverse temperature parameter beta distribution as well as the speed distribution this beta distribution has shown that the fluctuations in beta are distributed with respect to a chi square distribution it must be mentioned that two distinct tsallis q values are specified one is time dependent and the other is independent a ramification of these q values is that the highway segment and the traffic flow generate separate characteristics this highway segment in question is not only nonadditive in nature but a nonequilibrium driven system with frequent relaxations to a gaussian

general formalism for inhomogeneous random graphs we present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models where vertices come in different types and the probability of realizing an edge depends on the types of its terminal vertices this approach provides a general framework for the analysis of a large class of models the generic phase structure is derived using generating function techniques and relations to other classes of models are pointed out

fisher info and thermodynamics first law abstract we show starting from first principles that thermodynamics first law can be microscopically obtained for fisher s information measure without need of invoking the adiabatic theorem further it is proved that enforcing the fisher first law requirements in a process in which the probability distribution is infinitesimally varied is equivalent to minimizing fisher s information measure subject to appropriate constraints

an optimal consumption investment and voluntary retirement choice problem with disutility and subsistence consumption constraints a dynamic programming approach abstract in this paper we investigate an optimal consumption portfolio problem of an agent with voluntary retirement and subsistence consumption constraints before retirement we assume that the agent s utility function of consumption is of crra type and the agent suffers a utility loss from labor before retirement we use the dynamic programming method to obtain explicit forms of the optimal consumption portfolio and retirement time

stretched exponentials from superstatistics abstract distributions exhibiting fat tails occur frequently in many different areas of science a dynamical reason for fat tails can be a so called superstatistics where one has a superposition of local gaussians whose variance fluctuates on a rather large spatio temporal scale after briefly reviewing this concept we explore in more detail a class of superstatistics that hasn t been subject of many investigations so far namely superstatistics for which a suitable power of the local inverse temperature is 2 distributed we show that 0 leads to power law distributions while 0 leads to stretched exponentials the special case 1 corresponds to tsallis statistics and the special case 1 to exponential statistics of the square root of energy possible applications for granular media and hydrodynamic turbulence are discussed

a numerical scheme for a class of nonlinear fredholm integral equations of the second kind in this paper an iterative approach for obtaining approximate solutions for a class of nonlinear fredholm integral equations of the second kind is proposed the approach contains two steps at the first one we define a discretized form of the integral equation and prove that by considering some conditions on the kernel of the integral equation solution of the discretized form converges to the exact solution of the problem following that in the next step solution of the discretized form is approximated by an iterative approach we finally on some examples show the efficiency of the proposed approach

generalized superstatistics of nonequilibrium markovian systems abstract the paper is devoted to the construction of the superstatistical description for nonequilibrium markovian systems it is based on kirchhoff s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes the latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually then stationary probability as well as flux distributions are represented as some sums over the channels the latter construction actually forms the superstatistical description which however deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the boltzmann type

generalized box muller method for generating q gaussian random deviates the q gaussian distribution is known to be an attractor of certain correlated systems and is the distribution which under appropriate constraints maximizes a generalization of the familiar shannon entropy this generalized entropy or q entropy provides the basis of nonextensive statistical mechanics a theory which is postulated as a natural extension of the standard boltzmann gibbs statistical mechanics and which may explain the ubiquitous appearance of heavy tailed distributions in both natural and man made systems the q gaussian distribution is also used as a numerical tool for example as a visiting distribution in generalized simulated annealing a simple easy to implement numerical method for generating random deviates from a q gaussian distribution based upon a generalization of the well known box miiller method is developed and presented this method is suitable for a larger range of q values infin q 3 than has previously appeared in the literature and can generate deviates from q gaussian distributions of arbitrary width and center matlab code showing a straightforward implementation is also included

perturbation expansion for option pricing with stochastic volatility abstract we fit the volatility fluctuations of the s p 500 index well by a chi distribution and the distribution of log returns by a corresponding superposition of gaussian distributions the fourier transform of this is remarkably of the tsallis type an option pricing formula is derived from the same superposition of black scholes expressions an explicit analytic formula is deduced from a perturbation expansion around a black scholes formula with the mean volatility the expansion has two parts the first takes into account the non gaussian character of the stock fluctuations and is organized by powers of the excess kurtosis the second is contract based and is organized by the moments of moneyness of the option with this expansion we show that for the dow jones euro stoxx 50 option data a hedging strategy is close to being optimal

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

velocity structure functions scaling and transitions in high reynolds number couette taylor flow flow between concentric cylinders with a rotating inner cylinder is studied for reynolds numbers in the range 2 ifmmode times else texttimes fi 10 3 lrl 10 6 taylor reynolds numbers 10l r ensuremath lambda l290 for a system with radius ratio ensuremath eta 0 724 even at the highest reynolds number studied the energy spectra do not show power law scaling i e there is no inertial range and the dissipation length scale is surprisingly large nevertheless the velocity structure functions calculated using extended self similarity exhibit clear power law scaling the structure function exponents ensuremath zeta p fit kolmogorov s log normal model within the experimental uncertainty ensuremath zeta p p 3 1 ensuremath mu 6 3 ensuremath p for pl 10 with ensuremath mu 0 27 these ensuremath zeta p values are close to those found in other flows measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported lathrop et al phys rev a 46 6390 1992 measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest reynolds numbers examined these waves show evidence of a transition at r t 1 3 ifmmode times else texttimes fi 10 4 this transition was observed previously in measurements of torque but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at r t velocity measurements indicate that at r t there is a change in the coherent structures of the core flow this is consistent with our analyses of the scaling of the torque our measurements were made at two aspect ratios and no significant dependence on aspect ratio was observable for rg r t

piecewise continuous collocation for integral equations the collocation method for integral equations of the second kind is surveyed and analyzed for the case in which the approximate solutions are only piecewise continuous difficulties with the usual function space setting of l infty d are discussed and a satisfactory sense of point evaluation is given for elements of l infty d other approaches which are discussed include i reformulation as a degenerate kernel method ii the prolongation restriction framework of noble iii other function space settings and iv reformulation as a continuous approximation problem by iterating the piecewise continuous approximate solution in the original integral equation

coupled continuous time random walk approach to the rachev ruschendorf model for financial data abstract in this paper we expand the rachev ruschendorf asset pricing model introducing a coupled continuous time random walk ctrw like form of the random number of price changes such a form results from the concept of the random clustering procedure that resembles the coarse graining methods of statistical physics and on the other hand indicates applicability of the ctrw idea widely used in physics to model anomalous diffusion for describing financial markets in the framework of the proposed model we derive the limiting distributions of log returns and the corresponding pricing formulas for european call option in order to illustrate the obtained theoretical results we present their fitting with several sets of financial data

path integral approach to closed form option pricing formulas with applications to stochastic volatility and interest rate models we present a path integral method to derive closed form solutions for option prices in a stochastic volatility model the method is explained in detail for the pricing of a plain vanilla option the flexibility of our approach is demonstrated by extending the realm of closed form option price formulas to the case where both the volatility and interest rates are stochastic this flexibility is promising for the treatment of exotic options our analytical formulas are tested with numerical monte carlo simulations

modelling train delays with q exponential functions we demonstrate that the distribution of train delays on the british railway network is accurately described by q exponential functions we explain this by constructing an underlying superstatistical model

transition from lognormal to χ2 superstatistics for financial time series abstract share price returns on different time scales can be well modelled by a superstatistical dynamics here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales it is shown that while 2 superstatistics works well on a time scale of days on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics the system dynamics thus exhibits a transition from lognormal to 2 superstatistics as a function of time scale we discuss a more general model interpolating between both statistics which fits the observed data very well we also present results on correlation functions of the extracted superstatistical volatility parameter which exhibits exponential decay for returns on large time scales whereas for returns on small time scales there are long range correlations and power law decay

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

algebraic hyperbolic spline quasi interpolants and applications abstract in this paper a construction of marsden s identity for uah b splines i e uniform algebraic hyperbolic b splines is developed and a clear proof is given with the help of this identity quasi interpolant schemes that produce the space of algebraic hyperbolic functions are derived efficient quadrature rules based on integrating some of these quasi interpolant schemes are constructed and studied numerical results that illustrate the effectiveness of these rules are presented

pricing bounds for discrete arithmetic asian options under levy models abstract analytical bounds for asian options are almost exclusively available in the black scholes framework in this paper we derive bounds for the price of a discretely monitored arithmetic asian option when the underlying asset follows an arbitrary levy process explicit formulas are given for kou s model merton s model the normal inverse gaussian model the cgmy model and the variance gamma model the results are compared with the comonotonic upper bound existing numerical results monte carlo simulations and in the case of the variance gamma model with an existing lower bound the method outlined here provides lower and upper bounds that are quick to evaluate and more accurate than existing bounds

fluctuations of entropy and log normal superstatistics nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales superstatistics which is statistics of statistics with two largely separated time scales offers a consistent theoretical framework for such a description here a theory is developed for log normal superstatistics based on the fluctuation theorem for entropy changes as well as the maximum entropy method this gives novel physical insight into log normal statistics other than the traditional multiplicative random processes a comment is made on a possible application of the theory to the fluctuating energy dissipation rate in turbulence

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

from time series to superstatistics complex nonequilibrium systems are often effectively described by a statistics of a statistics in short a superstatistics we describe how to proceed from a given experimental time series to a superstatistical description we argue that many experimental data fall into three different universality classes chi2 superstatistics tsallis statistics chi2 inverse superstatistics and log normal superstatistics we discuss how to extract the two relevant well separated superstatistical time scales tau and t the probability density of the superstatistical parameter beta and the correlation function for beta from the experimental data we illustrate our approach by applying it to velocity time series measured in turbulent taylor couette flow which is well described by log normal superstatistics and exhibits clear time scale separation

comparison of optimal portfolios with and without subsistence consumption constraints abstract we present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion crra utility function by comparing the previous studies with and without the constraints expressed by the minimum consumption requirement the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly as a result the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset this implies that even though the agent who has a restriction on consumption retires with lower wealth level she invests more money near the retirement when her risk aversion lies inside a certain range

central limit theorem for a class of globally correlated random variables the standard central limit theorem with a gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions here we study this problem for similar interchangeable globally correlated random variables under these conditions a hierarchical set of equations is derived for the conditional transition probabilities this result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables depending on the correlation mechanisms and statistics of the single variables the corresponding sums are characterized by distinct probability densities for a class of urn models it is also possible to characterize their domain of attraction which as in the standard case is parametrized by the probability density of each random variable symmetric and asymmetric q gaussian attractors q 1 arise in a particular two state case of these urn models

superstatistics in random matrix theory abstract using the superstatistics method we propose an extension of the random matrix theory to cover systems with mixed regular chaotic dynamics unlike most of the other works in this direction the ensembles of the proposed approach are basis invariant but the matrix elements are not statistically independent spectral characteristics of the mixed systems are expressed by averaging the corresponding quantities in the standard random matrix theory over the fluctuations of the inverse variance of the matrix elements we obtain analytical expressions for the level density and the nearest neighbor spacing distributions for four different inverse variance distributions the resulting expressions agree with each other for small departures from chaos measured by an effective non extensivity parameter our results suggest among other things that superstatistics is suited only for the initial stage of transition from chaos to regularity

dynamical modelling of superstatistical complex systems abstract we show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series for this purpose we generalise the superstatistics concept and study a langevin equation with a memory kernel whose parameters fluctuate on a large time scale we show how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data as a main example we apply our method to velocity time series measured in high reynolds number turbulent taylor couette flow but the method can be applied to many other complex systems in a similar way

optimal consumption and portfolio selection problem with downside consumption constraints abstract we study a general optimal consumption and portfolio selection problem of an infinitely lived investor whose consumption rate process is subjected to downside constraint that is her consumption rate is greater than or equals to some positive constant we obtain the general optimal policies in an explicit form using martingale method and feynman kac formula we derive some numerical results of optimal consumption and portfolio in the special case of a constant relative risk aversion crra utility function

two cubic spline methods for solving fredholm integral equations abstract in this work we propose two methods based on the use of natural and quasi cubic spline interpolations for approximating the solution of the second kind fredholm integral equations convergence analysis is established some numerical examples are given to show the validity of the presented methods

determining the complexity of multi component conformal systems a platoon based approach abstract many systems in nature and engineering are composed of subsystems these subsystems may be formed in a linear planar or spatial array a typical example of these formations is a chain of vehicles known as platoon formation in traffic flow platoon formation of vehicles is a linear or planar formation of vehicles where a certain and a constant headway and sideway if applicable is provided in between every and each one of them it is argued in this paper that a well automated platoon formation of vehicles is an extreme case of conformity during this transformation from a many degrees of freedom formation to a solid object tsallis q value is computed to be ranging from one extreme case of q 3 to the other where q 1 when classified in terms of inverse temperatures of clearance fluctuations at one extreme of q 3 one observes unbounded fluctuations in clearance fluctuations so that inverse temperature distributions approach a dirac delta at the origin at the other extreme of q 1 fluctuations in clearance tend to zero asymptotically where a solid structure of agents vehicles emerges the transition from q 3 to q 1 is investigated through synthetic and experimental clearance fluctuations between the cars the results show that during the transition from q 3 to q 1 the platoon loses its many degrees of freedom dof of motion until a solid single object emerges authors assert that the tsallis q value of a platoon of vehicles is limited to 3 q 1

asymptotics of superstatistics superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable e g the inverse temperature they contain tsallis statistics as a special case we develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics a saddle point approximation is developed which relates this problem to a variational principle several examples are worked out in detail

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

on new conditions for evaluate long time scales in superstatistical time series in this article we introduce an additional condition for the criterion previously presented in order to extract the update time scale of the intensive parameter in superstatistical time series with these modifications such criterion is capable of evaluating the actual long time scale in addition the criterion permits a valuable way to verify whether the process under study is superstatistical or not

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

numerical method using cubic b spline for the heat and wave equation in the present paper the cubic b splines method is considered for solving one dimensional heat and wave equations a typical finite difference approach had been used to discretize the time derivative while the cubic b spline is applied as an interpolation function in the space dimension the accuracy of the method for both equations is discussed the efficiency of the method is illustrated by some test problems the numerical results are found to be in good agreement with the exact solution

optimal investment consumption and retirement choice problem with disutility and subsistence consumption constraints in this paper we consider a general optimal consumption portfolio selection problem of an infinitely lived agent whose consumption rate process is subject to subsistence constraints before retirement that is her consumption rate should be greater than or equal to some positive constant before retirement we integrate three optimal decisions which are the optimal consumption the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model we obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem we treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches we also derive closed forms of the optimal wealth processes before and after retirement some numerical examples are presented for the case of constant relative risk aversion crra utility class

superstatistics with cut off tails for financial time series abstract financial time series have been investigated to follow fat tailed distributions with truncations in order to identify the nature of such fluctuations we proposed a stochastic volatility model by incorporating the cut off effect in superstatistics then we confirm that the proposed stochastic model is capable of describing the statistical properties of real financial time series in addition we present an option pricing formula with respect to superstatistics a new type of anomalous fluctuations is also investigated based on the proposed stochastic model

superpositions of probability distributions probability distributions which can be obtained from superpositions of gaussian distributions of different variances v ensuremath sigma 2 play a favored role in quantum theory and financial markets such superpositions need not necessarily obey the chapman kolmogorov semigroup relation for markovian processes because they may introduce memory effects we derive the general form of the smearing distributions in v which do not destroy the semigroup property the smearing technique has two immediate applications it permits simplifying the system of kramers moyal equations for smeared and unsmeared conditional probabilities and can be conveniently implemented in the path integral calculus in many cases the superposition of path integrals can be evaluated much easier than the initial path integral three simple examples are presented and it is shown how the technique is extended to quantum mechanics

beyond boltzmann gibbs statistics maximum entropy hyperensembles out of equilibrium what is the best description that we can construct of a thermodynamic system that is not in equilibrium given only one or a few extra parameters over and above those needed for a description of the same system at equilibrium here we argue the most appropriate additional parameter is the nonequilibrium entropy of the system moreover we should not attempt to estimate the probability distribution of the system directly but rather the metaprobability or hyperensemble that the system is described by a particular probability distribution the result is an entropic distribution with two parameters one a nonequilibrium temperature and the other a measure of distance from equilibrium this dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium we deduce that in general large rare fluctuations become far more common as we move away from equilibrium

numerical solutions of second order matrix models using cubic matrix splines many studies of mechanical systems in engineering are based on second order matrix models this work discusses the second order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for the initial problem y x f x y x y x using matrix cubic splines without any dimensional increase an estimation of the approximation error the corresponding algorithm of our approach and some illustrative examples are presented

q gaussian distributions of leverage returns first stopping times and default risk valuations a b s t r a c t we study the probability distributions of daily leverage returns of 520 north american industrial companies that survive de listing during the financial crisis 2006 2012 we provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q gaussian distributions with the tsallis entropic parameter within the interval 1 q 2 the fat tails of the observed distributions imply a much higher probability of extreme movements in a company s leverage ratio than forecasted by the normal distribution q 1 motivated by these findings we develop a q gaussian generalization of traditional structural models of default derived exact analytical expressions for the probability distribution of a first stopping time and its intensity forecast significantly higher probability of default and much wider credit spreads at short time horizons our findings are broadly consistent with the results of empirical studies in equity markets and are essential for single name default forecasting as well as valuations of portfolio credit risk and economic capital which might be underestimated by a classic theory of diversified portfolio optimization

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

numerical solution of linear fredholm integral equation by using hybrid taylor and block pulse functions in this paper we use a combination of taylor and block pulse functions on the interval 0 1 that is called hybrid functions to estimate the solution of a linear fredholm integral equation of the second kind we convert the integral equation to a system of linear equations and by using numerical examples we show our estimation have a good degree of accuracy

complex networks emerging from fluctuating random graphs analytic formula for the hidden variable distribution in analogy to superstatistics which connects boltzmann gibbs statistical mechanics to its generalizations through temperature fluctuations complex networks are constructed from fluctuating erd os r enyi random graphs using a quantum mechanical method the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the poisson transformation as an example a static scale free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin

superstatistical generalizations of wishart laguerre ensembles of random matrices using beck and cohen s superstatistics we introduce in a systematic way a family of generalised wishart laguerre ensembles of random matrices with dyson index 1 2 and 4 the entries of the data matrix are gaussian random variables whose variancesfluctuate from one sample to another according to a certain probability density f and a single deformation parameter three superstatistical classes for f are usually considered 2 inverse 2 and log normal distributions while the first class already considered by two of the authors leads to a power law decay of the spectral density we here introduce and solve exactly a superposition of wishart laguerre ensembles with inverse 2 distribution the corresponding macroscopic spectral density is given by a deformation of the semi circle and marcenko pastur laws on a non compact support with exponential tails after discussing in detail the validity of wigner s surmise in the wishart laguerre class we introduce a generalised dependent surmise with stretched exponential tails which well approximates the individual level spacing distribution in the bulk the analytical results are in excellent agreement with numerical simulations to illustrate our findings we compare the 2 and inverse 2 class to empirical data from financial covariance matrices