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

the q deformed boson realization of representations of quantum universal enveloping algebras for q a root of unity i the case of uqsl l the properties of q deformed boson operators with non generic q q is a root of unity are analysed by using the representation theory method and their finite dimensional representations are thereby obtained based on this discussion reducibilities and decompositions of q deformed boson realized representations of quantum universal enveloping algebra uqsl l are studied for non generic cases the explicit matrix elements of some indecomposable representations are obtained on the q deformed fock spaces necessary details are provided for uqsl 2 and uqsl 3 in particular the lusztig operator extension of uqsl 2 is discussed in an explicit form

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

dynamical behavior of combined detrended cross correlation analysis methods in random walks and levy flights abstract in this paper the utility and the correlation technique of the detrended cross correlation analysis and the combined detrended cross correlation analysis methods are treated for the stochastic properties of the random walk and the levy flight via nucleotide sequence data data are extracted definitely from twelve genomic dna sequences humhbb 1 6 amazonmolly bushbaby cow dolphin elephant and tarsier of the genbank databank we mainly simulate and analyze scaling exponents for three methods in 1d and 2d random walks and levy flights to compare each other between one gene and the other gene in the twelve genomic dna sequences the value of the detrended cross correlation coefficient d c c a in humhbb3 and dolphin genes is shown the largest value 0 214 in the 1d levy flight with 1 5 compared to other sets the detrended cross correlation coefficient d c c a in humhbb4 and humhbb6 genes is shown the smallest value 0 231 in the 1d levy flight with 1 5 we particularly find that the combined detrended cross correlation coefficient c d c c a in the two cases of humhbb3 bushbaby and humhbb6 dolphin has the largest value 0 331 in the 1d random walk compared to other sets while that in humhbb3 tarsier and humhbb4 elephant has the smallest value 0 295 in the 1d levy flight with 1 5

remarks on the possible universal mechanism of the non linear long term autocorrelations in financial time series the paper consists of two parts i the empirical one where the non linear long term autocorrelations present in high frequency data extracting from the warsaw stock exchange were analyzed and ii theoretical one where predictions of our model quantitative finance 3 2003 201 physica a 2003 chem phys 284 2002 481 phys comm 147 2002 565 physica a 264 1999 84 physica a 264 1999 107 lecture notes in computer science 2657 2003 407 eur phys j b 33 2003 495 were shown and discussed this model introduces the possibility that the weierstrass hierarchical random walk can be occasionally intermitted by momentary localizations the localizations themselves are again described by the weierstrass process in other words this combined walk is a kind of the non separable generalized continuous time random walk formalism to adapt the model to the description of empirical data recorded at time horizon t 1min we applied a discretization procedure into the continuous time series produced by the model we observed that such a procedure generates the non linear long term autocorrelations even in the gaussian regime as turning points of the random walk trajectory are most often incommensurable with discretization time step these autocorrelations appear to be similar to those observed in the financial time series physica a 287 2000 396 physica a 299 2001 1 physica a 299 2001 16 physica a 299 2001 28 although single steps of the walker within continuous time are by definition uncorrelated our approach suggests a surprising origin of the non linear long term autocorrelations alternative to the one proposed very recently cf phys rev e 67 2003 021112 and refs therein although both approaches involve related variants of the well known ctrw formalism applied in yet many different branches of knowledge phys rep 158 1987 263 phys rep 195 1990 127 in a bunde s havlin eds fractals in science springer berlin 1995 pp 119 161

polynomial realization of the uq sl 3 gel fand weyl zetlin basis an explicit realization of the u uq sl 3 gel fand weyl zetlin gwz basis as polynomial functions in three variables real or complex is given this realization is obtained in two complementary ways first a known correspondence is used between the abstract gwz basis and explicit polynomials in the quantum subgroup u of the raising generators then an explicit construction is used of arbitrary lowest weight holomorphic representations of u in terms of three variables on which the generators of u are realized as q difference operators the application of the gwz corresponding polynomials in this realization of the lowest weight vector the function 1 produces the first realization of this gwz basis another realization of the gwz polynomial basis is found by the explicit diagonalization of the operators of isospin i2 third component of isospin iz and hypercharge in the same realization as q difference operators the result is that the eigenvectors can be written in terms of q hypergeometric

symmetries of clebsch gordan coefficients of the quantum group uq n permutation symmetries for clebsch gordan coefficients of the quantum group uq n and for uq n 1 reduced clebsch gordan coefficients of uq n are derived in particular the formula relating clebsch gordan coefficients for the tensor product tm1 tm2 with clebsch gordan coefficients for the tensor product with permuted representations tm1 and tm is obtained where tm is one of the irreducible representations in the decomposition of tm1 tm2 contrary to the classical case coefficients connecting these clebsch gordan coefficients depend on gel fand tsetlin patterns of one of irreducible representations this dependence is explicitly determined

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

dynamics of stock prices we show that the dynamics of stock prices can be accurately described as a continuous time random walk with a time dependent diffusion coefficient the time evolution of the diffusion coefficient can be derived from tick by tick databases provided the stock price is characterized in terms of a couple of values describing the best ask and the best bid we are then led to a finding and namely that the transition rate of the random walk process is different from the frequency of transactions our results allow us to obtain a fast and reliable determination of the diffusion coefficient and precisely confirm that fat tails in the distribution of price variations are due to volatility fluctuations

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

monotonic continuous time random walks with drift and stochastic reset events in this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes we focus our attention on monotonic continuous time random walks with a constant drift the process increases between the reset events either by the effect of the random jumps or by the action of the deterministic drift as a result of all these combined factors interesting properties emerge like the existence for any drift strength of a stationary transition probability density function or the faculty of the model to reproduce power law like behavior general formulas for two extreme statistics the survival probability and the mean exit time are also derived to corroborate in an independent way the results of the paper monte carlo methods were used these numerical estimations are in full agreement with the analytical predictions

spectral analysis of fractional hyperbolic diffusion equations with random data the paper studies the fundamental solutions to fractional in time hyperbolic diffusion equation or telegraph equations and their properties then it derives the exact solutions of the fractional hyperbolic diffusion equation with random data in terms of series expansions of isotropic in space spherical random fields on the unit sphere numerical illustration are presented to illustrate the theoretical results

q deformation of the lorentz group we describe a q deformation of the lorentz group in terms of a q deformation of the van der waerden spinor algebra

a quantum analog of the z algebra we define a natural quantum analog for the z algebra and which we refer to as the zq algebra by modding out the heisenberg algebra from the quantum affine algebra uq sl 2 with level k we discuss the representation theory of this zq algebra in particular we exhibit its reduction to a group algebra and to a tensor product of a group algebra with a quantum clifford algebra when k 1 and k 2 and thus we recover the explicit constructions of uq sl 2 standard modules as achieved by frenkel jing and bernard respectively moreover for arbitrary nonzero level k we show that the explicit basis for the simplest z generalized verma module as constructed by lepowsky and primc is also a basis for its corresponding zq module i e it is invariant under the q deformation for generic q we expect this zq algebra associated with uq sl 2 at level k to play the role of a dynamical symmetry in the off critical zk statistical models

toroidal and level 0 uq sln 1 actions on uq gln 1 modules 1 utilizing a braid group action on a completion of uq sln 1 an algebra homomorphism from the toroidal algebra uq sln 1 tor n 2 to a completion of uq gln 1 is obtained 2 the toroidal actions by saito induces a level 0 uq sln 1 action on level 1 integrable highest weight modules of uq sln 1 another level 0 uq sln 1 action was defined by jimbo et al in the case n 1 using the fact that the intertwiners of uq sln 1 modules are intertwiners of toroidal modules for an appropriate comultiplication the relation between these two level 0 uq sln 1 actions is clarified

biorthogonal coupling coefficients of uq n the coupling wigner clebsch gordan coefficients and their isofactors for the unitary quantum algebras uq n with the repeating irreducible representations in the coproduct decomposition are considered generalizing the u n case the biorthogonal systems of the uq n isofactors with the dual multiplicity labels are constructed by means of the recoupling technique in terms of the isofactors with simpler multiplicity structure a first construction correlated with the inverted littlewood richardson rules gives the bilinear combinations of isofactors after applying the proportionality of the q recoupling racah coefficients to the boundary q isofactors an alternative recursive construction gives the nonorthogonal q isofactors satisfying the most elementary boundary conditions and proportional to the uq n 1 recoupling coefficients for some less restricted values of parameters some multiplicity free and more general uq n recoupling coefficients are found the blocks bilinear combinations of which equal to the resubducing coefficients of the complementary chains of q algebras are proposed to use for the orthonormalization of some uq n biorthogonal isofactors including the general uq 3 case

possible origin of the non linear long term autocorrelations within the gaussian regime abstract in this work we extend the recently considered toy model of weierstrass or levy walks with varying velocity of the walker quantitative finance 3 2003 201 chem phys 284 2002 481 comp phys comm 147 2002 565 phys a 264 1999 84 phys a 264 1999 107 by introducing a more realistic possibility that the walk can be occasionally intermitted by its momentary localization the localizations themselves are again described by the weierstrass or levy process the direct empirical motivation for developing this combined model is for example the dynamics of financial high frequency time series or hydrological and even meteorological ones where variations of the index are randomly intermitted by flat intervals of different length exhibiting no changes in the activity of the system this combined weierstrass walks was developed in the framework of the non separable generalized continuous time random walk formalism developed very recently lecture notes comput sci 2657 2003 407 eur phys j b 33 2003 495 this non markovian two state walking localization model makes possible to cover by the unified treatment a broad band of known up to now types of non biased diffusion from the dispersive one over the normal enhanced ballistic and hyperdiffusion up to the richardson law of diffusion which defines here a part of the borderline which separates the latter from the levy ocean where the total mean square displacement of the walker diverges we observed that anomalous diffusion is characterized here by three fractional exponents one temporal characterizing the localized state and two temporal and spatial characterizing the walking one by considering successive dynamic even exponents we constructed a series of different diffusion phase diagrams on the plane defined by the temporal and spatial partial fractional dynamic exponents characterizing the walking state to adapt the model to the description of empirical data the discrete time series which are collected with a discrete time step we used in the continuous time series produced by the model a discretization procedure we observed that such a procedure generates in general long range non linear autocorrelations even in the gaussian regime which appear to be similar to those observed e g in the financial time series phys a 287 2000 396 phys a 299 2001 1 phys a 299 2001 16 phys a 299 2001 16 although single steps of the walker within continuous time are by definition uncorrelated this suggests a suprising origin of long range non linear autocorrelations alternative to the one proposed very recently cf mosaliver et al phys rev e 67 2003 021112 and refs therein although both approaches involve related variants of the well known continuous time random walk formalism applied yet in many different branches of knowledge phys rep 158 1987 263 phys rep 195 1990 127 in a bunde s havlin eds fractals in science springer berlin 1995 p 1

multiplicity free uq n coupling coefficients the coupling wigner clebsch gordan coefficients of the unitary quantum algebras uq n are considered the tensorial properties of the generator powers and their ordered products used in the explicit projectors and weight lowering procedures are established different expressions for the multiplicity free isofactors of uq n coupling coefficients those coupling an arbitrary and symmetric representations are derived explicit expression of the arbitrary isofactors in terms of their boundary values are proposed proportionality of the semistretched isofactors to the stretched q recoupling coefficients of uq n 1 q analogues of 9j symbols is demonstrated the stretched isofactors of uq 3 are expressed in terms of clebsch gordan coefficients of uq 2

real de sitter and conformal algebras in terms of q oscillators we express the cartan weyl basis of all quantum real d 4 de sitter and d 4 conformal algebras in terms of q deformed oscillators

model for interevent times with long tails and multifractality in human communications an application to financial trading social technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure it is well known that the interevent statistics observed in these contexts differs from the poissonian profile by being long tailed distributed with resting and active periods interwoven understanding mechanisms generating consistent statistics has therefore become a central issue the approach we present is taken from the continuous time random walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions we here analyze the intertransaction time intervals of several financial markets we observe that empirical data describe a subtle multifractal behavior our model explains this structure by taking the pausing time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks a stretched exponential kernel provides a multifractal profile valid for a certain limited range a suggested heuristic analytical profile is capable of covering a broader region

passive motion in dynamical disorder as a model for stock market prices abstract a new model for stock price fluctuations is proposed based upon an analogy with the motion of tracers in gaussian random fields as used in turbulent dispersion models and in studies of transport in dynamically disordered media analytical and numerical results for this model in a special limiting case of a single scale field show characteristics similar to those found in empirical studies of stock market data specifically short term returns have a non gaussian distribution with super diffusive volatility assuming a power law decay of the time correlation of the disorder the returns correlation decays rapidly but the correlation function of the absolute returns exhibits a slow power law decay the returns distribution converges towards gaussian over long times some important characteristics of empirical data are not however reproduced by the model notably the scaling of tails of the cumulative distribution function of returns implied volatilities for options pricing are found by numerical simulation

non integrable representations of the restricted quantum analogue of sl 3 the structure of irreducible representations of restricted at roots of unity is understood within the gelfand zetlin basis the latter needs a weakened definition for non integrable representations where the quadratic casimir operator of the quantum subalgebra is not completely diagonalized this is necessary in order to take into account the indecomposable modules that appear the set of redefined mixed states has a teepee shape inside the pyramid made with the whole representation

power law for the calm time interval of price changes abstract in this paper we describe a newly discovered statistical property of time series data for daily price changes we investigated quantitatively the calm time intervals of price changes for 800 companies listed in the tokyo stock exchange and for the nikkei 225 index in the 27 year period from january 1975 to december 2001 a calm time interval is defined as the interval between two successive price changes above a fixed threshold we found that the calm time interval distribution of price changes obeys a power law decay furthermore we show that the power law exponent monotonically decreases with respect to the threshold

singular vectors of representations of quantum groups the author gives explicit formulae for singular vectors of verma modules over uq g they give the general formula for g an for some cases when g dn and for some rank two subalgebras of g not an dn for this he uses a special basis of uq g where g is the negative root subalgebra of g which was introduced in his earlier work on the case q 1 this basis seems more economical than the poincare birkhoff witt type of basis used by malikov feigin and fuchs 1986 for the construction of singular vectors of verma modules in the case q 1 furthermore this basis turns out to be part of a general basis introduced recently for other reasons by lusztig 1988 for uq b where b is a borel subalgebra of g

memory based persistence in a counting random walk process this paper considers a memory based persistent counting random walk based on a markov memory of the last event this persistent model is a different than the weiss persistent random walk model however leading thereby to different results we point out to some preliminary result in particular we provide an explicit expression for the mean and the variance both nonlinear in time of the underlying memory based persistent process and discuss the usefulness to some problems in insurance finance and risk analysis the motivation for the paper arose from the counting of events whether rare or not in insurance that presume that events are time independent and therefore based on the poisson distribution for counting these events

uncoupled continuous time random walk finite jump length probability density function in this work the uncoupled continuous time random walk model with the exponential jump length probability density function pdf is considered exact solutions for the pdf and second moment are obtained and investigated for different kinds of waiting time pdf

the ctrw in finance direct and inverse problems with some generalizations and extensions we study financial distributions within the framework of the continuous time random walk ctrw we review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non markovian formulation of the ctrw aimed to account for correlated increments of the return

classical invariant theory for the quantum symplectic group in this paper we establish the quantum analogues of the first and second fundamental theorem for vector invariants for the symplectic group let us briefly recall this result consider a vector space v endowed with a non degenerate antisymmetric bilinear form let sp v denote the group of isometries the first and second fundamental theorems for vector invariants for sp v tells us that any invariant polynomial function on

differential operators on quantized flag manifolds at roots of unity abstract the quantized flag manifold which is a q analogue of the ordinary flag manifold is realized as a non commutative scheme and we can define the category of d modules on it using the framework of non commutative algebraic geometry however when the parameter q is a root of unity lusztig s frobenius morphism allows us to handle d modules on the quantized flag manifold through modules over a certain sheaf of rings on the ordinary flag manifold in this paper we will show that this sheaf of rings on the ordinary flag manifold is an azumaya algebra over its center we also show that its restriction to certain subsets are split azumaya algebras these are analogues of some results of bezrukavnikov mirkovic rumynin on d modules on flag manifolds in positive characteristics

quantum line bundles on s2 and method of orbits for suq 2 the quantum sphere is covered by two quantum complex planes quantum line bundle on s2 is introduced by specifying a transition function the structure of the quantum complex planes enables one to construct representations of suq 2 acting in spaces of holomorphic sections in the quantum case dressing transformation replaces coadjoint action

continuous time random walk model for financial distributions we apply the formalism of the continuous time random walk to the study of financial data the entire distribution of prices can be obtained once two auxiliary densities are known these are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump we have applied the formalism to data on the u s dollar deutsche mark future exchange finding good agreement between theory and the observed data

the distribution of first passage times and durations in forex and future markets abstract possible distributions are discussed for intertrade durations and first passage processes in financial markets the view point of renewal theory is assumed in order to represent market data with relatively long durations two types of distributions are used namely a distribution derived from the mittag leffler survival function and the weibull distribution for the mittag leffler type distribution the average waiting time residual life time is strongly dependent on the choice of a cut off parameter t max whereas the results based on the weibull distribution do not depend on such a cut off therefore a weibull distribution is more convenient than a mittag leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations on the other hand we find that the gini index is rather independent of the cut off parameter based on the above considerations we propose a good candidate for describing the distribution of first passage time in a market the weibull distribution with a power law tail this distribution compensates the gap between theoretical and empirical results more efficiently than a simple weibull distribution it should be stressed that a weibull distribution with a power law tail is more flexible than the mittag leffler distribution which itself can be approximated by a weibull distribution and a power law indeed the key point is that in the former case there is freedom of choice for the exponent of the power law attached to the weibull distribution which can exceed 1 in order to reproduce decays faster than possible with a mittag leffler distribution we also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory moreover we discuss the limitation of our distributions by applying our distribution to the analysis of the btp future and calculating the average waiting time we find that our distribution is applicable as long as durations follow a weibull law for short times and do not have too heavy a tail

uncoupled continuous time random walks solution and limiting behavior of the master equation a detailed study is presented for a large class of uncoupled continuous time random walks ctrws the master equation is solved for the mittag leffler survival probability the properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed finally some common objections found in the literature are thoroughly reviewed

stochastic volatility of financial markets as the fluctuating rate of trading an empirical study we present an empirical study of the subordination hypothesis for a stochastic time series of a stock price the fluctuating rate of trading is identified with the stochastic variance of the stock price as in the continuous time random walk ctrw framework the probability distribution of the stock price changes log returns for a given number of trades n is found to be approximately gaussian the probability distribution of n for a given time interval dt is nonpoissonian and has an exponential tail for large n and a sharp cutoff for small n combining these two distributions produces a non trivial distribution of log returns for a given time interval dt which has exponential tails and a gaussian central part in agreement with empirical observations r 2007 elsevier b v all rights reserved

quantumr matrices related to the spin representations ofbn anddn we present the explicit form of the trigonometricr matrices related to the spin representations of the simple lie algebrasx n b n d n we conjecture that one dimensional configuration sums of the corresponding vertex models in the face formulation are the string functions ofx 1 modules

asymptotic solutions of decoupled continuous time random walks with superheavy tailed waiting time and heavy tailed jump length distributions we study the long time behavior of decoupled continuous time random walks characterized by superheavy tailed distributions of waiting times and symmetric heavy tailed distributions of jump lengths our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time we show that the probability density of the scaled walker position converges in the long time limit to a nondegenerate one only if the scaling function behaves in a certain way this function as well as the limiting probability density are determined in explicit form also we express the limiting probability density which has heavy tails in terms of the fox h function and find its behavior for small and large distances

the spin 1 2xxz heisenberg chain the quantum algebra uq sl 2 and duality transformations for minimal models the finite size scaling spectra of the spin 1 2 xxz heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c 1 including the unitary and nonunitary minimal series taking into account the half integer angular momentum sectors which correspond to chains with an odd number of sites in many cases leads to new spinor operators appearing in the projected systems these new sectors in the xxz chain correspond to new types of frustration lines in the projected minimal models the corresponding new boundary conditions in the hamiltonian limit are investigated for the ising model and the 3 state potts model and are shown to be related to duality transformations which are an additional symmetry at their self dual critical point by different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite xxz chain the observed degeneracies in the energy and momentummore spectra are shown to be the consequence of intertwining relations involving u sub q sl 2 quantum algebra transformations 35 refs 3 tabs less

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

raising and lowering operators for uq n after reviewing the defining relations for the gq algebra uq n the author constructs a cartan weyl basis and lists the q commutation relations of its generators he then uses the latter to explicitly construct sets of raising and lowering operators for the canonical chain of q algebras uq n uq n 1 generalizing those introduced by nagel and moshinsky 1965 for u m u n 1 finally he gives their normalization coefficients and shows how the normalized operators can be used to go from any gel fand tseitlin basis state that is of highest weight in uq n 1 to any other one and ultimately to construct the whole gel fand tseitlin basis from its highest weight state this work both generalizes a previous work of ueno et al 1989 on lowering operators and provides explicit expressions for their operators in terms of uq n cartan weyl generators

scaling in the distribution of intertrade durations of chinese stocks abstract the distribution of intertrade durations defined as the waiting times between two consecutive transactions is investigated based upon the limit order book data of 23 liquid chinese stocks listed on the shenzhen stock exchange in the whole year 2003 a scaling pattern is observed in the distributions of intertrade durations where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve the scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions the ensemble distributions for all stocks are modeled by the weibull and the tsallis q exponential distributions maximum likelihood estimation shows that the weibull distribution outperforms the q exponential for not too large intertrade durations which account for more than 98 5 of the data alternatively nonlinear least squares estimation selects the q exponential as a better model in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities the distribution of intertrade durations is weibull followed by a power law tail with an asymptotic tail exponent close to 3

limiting distributions of continuous time random walks with superheavy tailed waiting times we study the long time behavior of the scaled walker particle position associated with decoupled continuous time random walks which is characterized by superheavy tailed distribution of waiting times and asymmetric heavy tailed distribution of jump lengths both the scaling function and the corresponding limiting probability density are determined for all admissible values of tail indexes describing the jump distribution to analytically investigate the limiting density function we derive a number of different representations of this function and in this way establish its main properties we also develop an efficient numerical method for computing the limiting probability density and compare our analytical and numerical results

continuous time random walks under power law resetting we study continuous time random walks ctrw with power law distribution of waiting times under resetting which brings the walker back to the origin with a power law distribution of times between the resetting events two situations are considered under complete resetting the ctrw after the resetting event starts anew with a new waiting time independent of the prehistory under incomplete resetting the resetting of the coordinate does not influence the waiting time until the next jump we focus on the behavior of the mean squared displacement msd of the walker from its initial position on the conditions under which the probability density functions of the walker s displacement show universal behavior and on this universal behavior itself we show that the behavior of the msd is the same as in the scaled brownian motion sbm being the mean field model of the ctrw the intermediate asymptotics of the probability density functions pdf for ctrw under complete resetting provided they exist are also the same as in the corresponding case for sbm for incomplete resetting however the behavior of the pdf for ctrw and sbm is vastly different

domain boundary energies in finite regions at 2d criticality via conformal field theory by use of conformal field theory the authors calculate universal results for the energies of curved domain boundaries at two dimensional critical points in circular and rectangular regions this work extends the theory of finite size effects at criticality complementing previous exact results for the energies of domain boundaries in infinite strips

generalized diffusion equation and analytical expressions to neutron scattering experiments abstract an integro differential diffusion equation with linear force based on the continuous time random walk model is considered the equation generalizes the ordinary and fractional diffusion equations analytical expressions related to neutron scattering experiments are presented and analyzed which can be used to describe for instance biological systems

diffusion entropy technique applied to the study of the market activity abstract the present work briefly summarizes the results obtained in palatella et al eur phys j b 38 2004 671 using the diffusion entropy technique and adds some new results regarding the dow jones index time series we show that time distances between peaks of volatility or activity are distributed following an asymptotic power law which ultimately recovers an exponential behavior we discuss these results in comparison with the tarch model the ornstein uhlenbeck stochastic volatility model and a multi agent model we conclude that both arch and stochastic volatility models better describe the observed experimental evidences

numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term in this paper we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term a new implicit difference method is constructed the stability and convergence are discussed using a new energy method finally some numerical examples are given the numerical results demonstrate the effectiveness of theoretical analysis

solution of a modified fractional diffusion equation abstract recently a modified fractional diffusion equation has been proposed i sokolov j klafter from diffusion to anomalous diffusion a century after einstein s brownian motion chaos 15 2005 026103 a v chechkin r gorenflo i m sokolov v yu gonchar distributed order time fractional diffusion equation frac calc appl anal 6 3 2003 259279 i m sokolov a v checkin j klafter distributed order fractional kinetics acta phys pol b 35 2004 1323 for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term in this letter we give the solution of the modified equation on an infinite domain in contrast to the solution of the traditional fractional diffusion equation the solution of the modified equation requires an infinite series of fox functions instead of a single fox function

normalized uq sl 3 gel fand weyl zetlin basis and new summation formulas for q hypergeometric functions an explicit realization of the normalized gel fand weyl zetlin gwz basis for uq sl 3 in terms of polynomial functions in three variables real or complex is given the construction uses two different realizations of the uq sl 3 unnormalized gwz basis which were given previously and whose transformation properties were not known it turns out that finding these properties enables us to find the gwz dependent proportionality constant between these two realizations the scalar product is also fixed by this in both unnormalized realizations and then by normalization the normalized gwz states are obtained as by products new summation formulas are obtained which seem new also for q 1 the main new formula is a double sum which is given in terms of the proportionality constant mentioned above this double sum can be written as single sum over a q 3f2 hypergeometric function or as a q hypergeometric function of two variables

intra day variability of the stock market activity versus stationarity of the financial time series abstract in this paper we propose a new approach to a well known phenomena of intra day activity pattern on the stock market we suggest that seasonality of inter transaction times has a more significant impact than intra day pattern of volatility our aim is not to remove the intra day pattern from the data but to describe its impact on autocorrelation function estimators we obtain an exact analytical formula relating estimators of the autocorrelation functions of non stationary seasonal process to its stationary counterpart hence we prove that the day seasonality of inter transaction times extends the memory of the process that is autocorrelation of both price returns and their absolute values relaxation to zero is longer

crossing probabilities in critical 2 d percolation and modular forms abstract crossing probabilities for critical 2 d percolation on large but finite lattices have been derived via boundary conformal field theory these predictions agree very well with numerical results however their derivation is heuristic and there is evidence of additional symmetries in the problem this contribution gives a preliminary examination some unusual modular behavior of these quantities in particular the derivatives of the horizontal and horizontal vertical crossing probabilities transform as a vector modular form one component of which is an ordinary modular form and the other the product of a modular form with the integral of a modular form we include consideration of the interplay between conformal and modular invariance that arises

quantization of lie group and algebra of g2 type in the faddeev reshetikhin takhtajan approach based on the quantized universal enveloping que algebras a quantization of the automorphism group of some nonassociative algebras is given in the formulation employing noncommuting matrix entries a quantum group of g2 type included in this scheme is studied in detail in the faddeev reshetikhin takhtajan frt approach also in the formulation employing noncommuting matrix entries the que algebra of g2 type is reconstructed through the pairing induced by the r matrix between the quantum group and the que algebra

real function inequalities from conformal maps we establish several new inequalities for real functions that are the restriction to the real axis of conformal maps of the upper half plane into itself our various results involve the average derivatives geometric mean derivatives cross ratios and schwarzian derivatives of such functions connections with the hyperbolic metric and theory of monotone matrix functions are mentioned applications to conformal field theory two dimensional phase transitions and special functions are made

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

extremal behavior of a coupled continuous time random walk abstract coupled continuous time random walks ctrws model normal and anomalous diffusion of random walkers by taking the sum of random jump lengths dependent on the random waiting times immediately preceding each jump they are used to simulate diffusion like processes in econophysics such as stock market fluctuations where jumps represent financial market microstructure like log returns in this and many other applications the magnitude of the largest observations e g a stock market crash is of considerable importance in quantifying risk we use a stochastic process called a coupled continuous time random maxima ctrm to determine the density governing the maximum jump length of a particle undergoing a ctrw ctrm are similar to continuous time random walks but track maxima instead of sums the many ways in which observations can depend on waiting times can produce an equally large number of ctrm governing density shapes we compare densities governing coupled ctrm with their uncoupled counterparts for three simple observation wait dependence structures

a classification of unitary highest weight modules of the quantum analogue of the symmetric pair an an 1 abstract we study the irreducibility and unitarity of highest weight modules of the quantized enveloping algebra associated to s u n 1 we obtain a classification of these modules analogous to that of ehw in the classical context we also compute all commutation relations between root vectors in u q s u n 1

dynamical structures of high frequency financial data abstract we study the dynamical behavior of high frequency data from the korean stock price index kospi using the movement of returns in korean financial markets the dynamical behavior of a binarized series of our models is not completely random in addition the conditional probability is numerically estimated from a return series of kospi tick data non trivial probability structures can be constituted from binary time series of autoregressive ar logit and probit models for which the akaike information criterion shows a minimum value at the 15th order from our results we find that the value of the correct match ratio for the ar model is slightly larger than that derived by other models

q analogs of iu n and u n 1 the starting point is the nonsemisimple inhomogeneous lie algebra un i2n denoted also as iu n where i2n represents an abelian subalgebra in semidirect product with the homogeneous part u n this is realized by explicitly giving the matrix elements of the generators on a modified gelfand zetlin basis that allows representations of infinite dimensions the enveloping algebra is q lifted by introducing q brackets in the matrix elements giving uq iu n the deformation of the abelian structure of i2n is studied for q 1 some implications are pointed out the important invariants are constructed for arbitrary n the results are compared to the corresponding ones for jimbo s construction of uq u n 1 on a gelfeld zetlin basis finally the related construction of uq u n 1 is presented and discussed here uq su 1 1 the q analog of relativistic motion in a plane is analyzed in the context of this formalism

irregular uq sl 3 representations at roots of unity via gel fand weyl zetlin basis the gel fand weyl zetlin gwz description of the uq sl 3 irregular irreps at roots of unity is explicitly given those are irreps fixed by the same parameters as the unitary irreducible representations uirs of su 3 yet having dimensions smaller than their classical counterparts the reason being that to obtain an irregular irrep one has to make factorization of an additional submodule this description is made geometrically transparent by an arrangement of the standard su 3 gwz basis in a hexagonal pyramid which is valid for any q and seems new even for q 1 the pyramid has as a base the standard hexagon which gives the weight space of the uirs of su 3 in the plane of third component of isospin iz and hypercharge y while third dimension of this pyramid is related to the isospin i algebraically this arrangement is related to a one to one correspondence between the abstract gwz states and monomials in the algebra of raising generators uq g however those monomials are not in the standard poi

modeling non stationarities in high frequency financial time series abstract we study tick by tick financial returns for the ftse mib index of the italian stock exchange borsa italiana we confirm previously detected non stationarities scaling properties reported before for other high frequency financial data are only approximately valid as a consequence of our empirical analyses we propose a simple model for non stationary returns based on a non homogeneous normal compound poisson process it turns out that our model can approximately reproduce several stylized facts of high frequency financial time series moreover using monte carlo simulations we analyze order selection for this class of models using three information criteria akaike s information criterion aic the bayesian information criterion bic and the hannan quinn information criterion hq for comparison we perform a similar monte carlo experiment for the acd autoregressive conditional duration model our results show that the information criteria work best for small parameter numbers for the compound poisson type models whereas for the acd model the model selection procedure does not work well in certain cases

correlated continuous time random walk and option pricing in this paper we study a correlated continuous time random walk cctrw with averaged waiting time whose probability density function pdf is proved to follow stretched gaussian distribution then we apply this process into option pricing problem supposing the price of the underlying is driven by this cctrw we find this model captures the subdiffusive characteristic of financial markets by using the mean self financing hedging strategy we obtain the closed form pricing formulas for a european option with and without transaction costs respectively at last comparing the obtained model with the classical black scholes model we find the price obtained in this paper is higher than that obtained from the black scholes model a empirical analysis is also introduced to confirm the obtained results can fit the real data well

free energy of rectangular domains at criticality the authors calculate the universal part f of the free energy of rectangular domains at critical points by use of conformal field theory f includes a term logarithmic in the size or area due to the corners in addition there is a term f0 depending on the aspect ratio which they determine by integrating the stress tensor t over the rectangle this term involves complete elliptic integrals but may be more simply expressed in terms of the dedekind eta function for central charge c 0 they find that f0 is maximal for squares providing a thermodynamic driving force for the elongation of small domains and argue that this should be a general tendency