tempered stable levy motion and transient super diffusion the space fractional diffusion equation models anomalous super diffusion its solutions are transition densities of a stable levy motion representing the accumulation of power law jumps the tempered stable levy motion uses exponential tempering to cool these jumps a tempered fractional diffusion equation governs the transition densities which progress from super diffusive early time to diffusive late time behavior this article provides finite difference and particle tracking methods for solving the tempered fractional diffusion equation with drift a temporal and spatial second order crank nicolson method is developed based on a finite difference formula for tempered fractional derivatives a new exponential rejection method for simulating tempered levy stables is presented to facilitate particle tracking codes

on initial boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order abstract for the nonlinear hyperbolic equation u 2 1 f x t u u 1 0 u 2 0 u 0 1 u 1 1 problems on bounded solutions in a half strip and in a strip are studied unimprovable conditions of local and global solvability and unique solvability of these problems are established

surmounting oscillating barriers path integral approach for weak noise we consider the thermally activated escape of an overdamped brownian particle over a potential barrier in the presence of periodic driving a time dependent path integral formalism is developed which allows us to derive asymptotically exact weak noise expressions for both the instantaneous and the time averaged escape rate our results comprise a conceptually different systematic treatment of the rate prefactor multiplying the exponentially leading arrhenius factor moreover an estimate for the deviations at finite noise strengths is provided and a supersymmetry type property of the time averaged escape rate is verified for piecewise parabolic potentials the rate expression can be evaluated in closed analytical form while in more general cases as exemplified by a cubic potential an action integral remains to be minimized numerically our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies

entropy and boundary conditions in random rhombus tilings the tilings of rhombi in two dimensions and of rhomboedra in three dimensions are studied when they are constrained by fixed boundary conditions we establish a link between those conditions and free or periodic boundary ones the entropy is written as a functional integral which is treated via a saddle point method we can exhibit the dominant states of the statistical ensemble of tilings and show that they can display a strong structural inhomogeneity caused by the boundary this inhomogeneity is responsible for a difference of entropy between the studied fixed boundary tilings and free boundary ones this method uses a representation of tilings by membranes embedded in a higher dimensional hypercubic lattice it is illustrated in the case of 60 degree rhombus tilings

the square triangle random tiling model in the thermodynamic limit the thermodynamic limit for the square triangle random tiling model is considered the analytic solution of the bethe ansatz equations found recently by widom 1993 is obtained the analytic expression for entropy density as a function of the fraction of the plane occupied by triangles alpha t is derived for the case alpha t or 1 2 i e for the phason gradients having 6 fold symmetry including 12 fold symmetric phase as the limiting case the exact values for phason elastic constants are also found

arma model identification of hydrologic time series in recent years arma models have become popular for modeling geophysical time series in general and hydrologic time series in particular the identification of the appropriate order of the model is an important stage in arma modeling such model identification is generally based on the autocorrelation and partial autocorrelation functions although recently improvements have been obtained using the inverse autocorrelation and the inverse partial autocorrelation functions this paper demonstrates the use of the generalized partial autocorrelation function gpaf and the r and s functions of gray et al 1978 for arma model identification of hydrologic time series these functions are defined and some recursive relations are given for ease of computation all three functions when presented in tabular form have certain characteristic patterns that are useful in arma model identification several examples are included to demonstrate the usefulness of the proposed identification technique actual applications are made using the saint lawrence river and nile river annual streamflow series

two point higher order bvps with singularities in phase variables the existence of solutions for singular higher order differential equations with the lidstone or the n p boundary conditions is proved the right hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities proofs are based on the method of a priori estimates the degree theory arguments and on vitali s convergence theorem

diffractive point sets with entropy after a brief historical survey this paper introduces the notion of entropic model sets cut and project sets and more generally the notion of diffractive point sets with entropy such sets may be thought of as generalizations of lattice gases we show that taking the site occupation of a model set stochastically results with probabilistic certainty in well defined diffractive properties augmented by a constant diffuse background we discuss both the case of independent but identically distributed i i d random variables and that of independent but different i e site dependent random variables several examples are shown

random growth of interfaces as a subordinated process we study the random growth of surfaces from within the perspective of a single column namely the fluctuation of the column height around the mean value y t identical with h t which is depicted as being subordinated to a standard fluctuation dissipation process with friction gamma we argue that the main properties of kardar parisi zhang theory in one dimension are derived by identifying the distribution of return times to y 0 0 which is a truncated inverse power law with the distribution of subordination times the agreement of the theoretical prediction with the numerical treatment of the 1 1 dimensional model of ballistic deposition is remarkably good in spite of the finite size effects affecting this model

phase diagram of a random tiling quasicrystal we study the phase diagram of a two dimensional random tiling model for quasicrystals at proper concentrations the model has 8 fold rotational symmetry landau theory correctly gives most of the qualitative features of the phase diagram which is in turn studied in detail numerically using a transfer matrix approach we find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first order or continuous transitions exact solutions are given in all phases except for the quasicrystal phase and for the phase boundaries between them we calculate numerically the phason elastic constants and entropy density and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8 fold rotational symmetry in addition to the obvious application to quasicrystals this study generalizes certain surface roughening models to two dimensional surfaces in four dimensions

solution of the dimer problem on a hexagonal lattice with boundary the dimer problem is solved exactly for a hexagonal lattice with general boundary using a known generating function from the theory of partitions it is shown that the leading term in the entropy depends on the shape of the boundary

subordinated continuous time ar processes and their application to modeling behavior of mechanical system abstract many real data exhibit behavior adequate to subdiffusion processes very often it is manifested by so called trapping events the visible evidence of subdiffusion we observe not only in financial time series but also in technical data in this paper we propose a model which can be used for description of such kind of data the model is based on the continuous time autoregressive time series with stable noise delayed by the infinitely divisible inverse subordinator the proposed system can be applied to real datasets with short time dependence visible jumps and mentioned periods of stagnation in this paper we extend the theoretical considerations in analysis of subordinated processes and propose a new model that exhibits mentioned properties we concentrate on the main characteristics of the examined subordinated process expressed mainly in the language of the measures of dependence which are main tools used in statistical investigation of real data we present also the simulation procedure of the considered system and indicate how to estimate its parameters the theoretical results we illustrate by the analysis of real technical data

on solvability of boundary value problems for higher order nonlinear hyperbolic equations abstract in the rectangle 0 a 0 b for the nonlinear hyperbolic equation u m n i 0 m 1 h 1 i x u i n k 0 n 1 h 2 k y u m k f x y u u m 1 n 1 the boundary value problems of the type l 1 i u y 0 i 1 m l 2 k u x 0 k 1 n are considered where l 1 i c m 1 0 a r i 1 m and l 2 k c n 1 0 b r k 1 n are linear bounded functionals sufficient conditions of solvability and unique solvability of the general problem and its particular cases nicoletti type dirichlet lidstone and periodic problems are established

current fluctuations in stochastic systems with long range memory we propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history dependent rates long range temporal correlations are seen to alter the speed of the large deviation function in analogy with long range spatial correlations in equilibrium systems we give some illuminating examples and discuss the applicability of the gallavotti cohen fluctuation theorem

boundary conditions entropy and the signature of random tilings we investigate the influence of boundary conditions on the results of monte carlo simulations of 2d random tilings looking at the fluctuations in internal space we compare fixed and periodic boundaries we find that fixed boundary conditions will lead to a different random tiling ensemble with reduced finite size entropy density in comparison with periodic boundary conditions as a by product we derive improved estimates for the elastic constants of the octagonal rhombus tiling ensemble finally we introduce a robust tool also suitable for the analysis of experimental data to distinguish between quasiperiodic and random tiling models

kramers escape problem for fractional klein kramers equation with tempered α stable waiting times in this paper we extend the subdiffusive klein kramers model in which the waiting times are modeled by the stable laws to the case of waiting times belonging to the class of tempered stable distributions we introduce a generalized version of the klein kramers equation in which the fractional riemman liouville derivative is replaced with a more general integro differential operator this allows a transition from the initial subdiffusive character of motion to the standard diffusion for long times to be modeled taking advantage of the corresponding langevin equation we study some properties of the tempered dynamics in particular we approximate solutions of the tempered klein kramers equation via monte carlo methods also we study the distribution of the escape time from the potential well and compare it to the classical results in the kramers escape theory finally we derive the analytical formula for the first passage time distribution for the case of free particles we show that the well known sparre andersen scaling holds also for the tempered subdiffusion

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

diffusion and relaxation controlled by tempered α stable processes we derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha stable processes the tempering results in the existence of all moments of operational time the subordination by the inverse tempered alpha stable process provides diffusion relaxation that occupies an intermediate place between subdiffusion cole cole law and normal diffusion exponential law here we obtain explicitly the fokker planck equation and the cole davidson relaxation function this model includes subdiffusion as a particular case

bivariate sub gaussian model for stock index returns abstract financial time series are commonly modeled with methods assuming data normality however the real distribution can be nontrivial also not having an explicitly formulated probability density function in this work we introduce novel parameter estimation and high powered distribution testing methods which do not rely on closed form densities but use the characteristic functions for comparison the approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub gaussian distribution the methods presented here can be applied to any nontrivially distributed financial data among others

random tilings of high symmetry ii boundary conditions and numerical studies we perform numerical studies including monte carlo simulations of high rotational symmetry random tilings for computational convenience our tilings obey fixed boundary conditions in regular polygons such tilings are put in correspondence with algorithms for sorting lists in computer science we obtain statistics on path counting and vertex coordination which compare well with predictions of mean field theory and allow estimation of the configurational entropy which tends to the value 0 568 per vertex in the limit of continuous symmetry tilings with phason strain appear to share the same entropy as unstrained tilings as predicted by mean field theory we consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy although these differ for finite rotational symmetry

random tilings concepts and examples we introduce a concept for random tilings which comprising the conventional one is also applicable to tiling ensembles without height representation in particular we focus on the random tiling entropy as a function of the tile densities in this context and under rather mild assumptions we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble explicit examples are obtained through the re interpretation of several exactly solvable models this also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum

fractional brownian motion time changed by gamma and inverse gamma process abstract many real time series exhibit behavior adequate to long range dependent data additionally very often these time series have constant time periods and also have characteristics similar to gaussian processes although they are not gaussian therefore there is need to consider new classes of systems to model these kinds of empirical behavior motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena both of them are constructed as the superposition of fractional brownian motion fbm and other process in the first case the internal process which plays role of the time is the gamma process while in the second case the internal process is its inverse we present in detail their main properties paying main attention to the long range dependence property moreover we show how to simulate these processes and estimate their parameters we propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process this method is very useful in description of rounded data like waiting times of subordinated processes delayed by inverse subordinators by using the monte carlo method we show the effectiveness of proposed estimation procedures finally we present the applications of proposed models to real time series

a generalized fokker planck equation for particle transport in random media abstract a transport equation is derived for the probability density function pdf that gives the phase space distribution of a particle moving in a random medium the motion of the particle is determined by a general second order stochastic differential equation that models transport in a medium exhibiting correlated fluctuations in both space and time the derivation makes use of cumulant expansions and functional calculus the most general form of the transport equation requires closure and a simple closure approximation is discussed no closure approximation is necessary when the stochastic component of the particle equation of motion is a correlated gaussian process and results for transport in an unbounded medium are derived for this exact case these results are consistent with other studies and serve to validate the model

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

h theorems for the brownian motion on the hyperbolic plane abstract we study h theorems associated with the brownian motion with constant drift on the hyperbolic plane since this random process satisfies a linear fokker planck equation it is easy to show that up to a proper scaling its shannon entropy is increasing over time as a consequence its distribution is converging to a maximum shannon entropy distribution which is also shown to be related to the non extensive statistics in a second part relying on a theorem by shiino we extend this result to the case of tsallis entropies we show that under a variance like constraint the tsallis entropy of the brownian motion on the hyperbolic plane is increasing provided that the non extensivity parameter of this entropy is properly chosen in terms of the drift of the brownian motion

properties of diffusive systems near a saddle point application to a quartic double well this paper aims at the analysis of diffusive properties of unidimensional mechanical systems in the environment of maxima and minima of the potential it begins with a study of the properties of the singular solutions of the hamilton jacobi yasue equation in the above mentioned environment in both strong or very small frictional forces for the quartic symmetrical double well potential approximate solutions are found for local validity and the diffusion operator is then calculated in the limits of deep wells and small temperature the regime being supposed to be aperiodic with high or moderate values of frictional coefficient this equation is proved to be nonunique this operator is then reduced to second order by imposing suitable boundary conditions thus an appropriate eigenvalue equation is obtained to describe stationary states in the environment of extremal points of the potential energy function the main interest of this work relies upon the fact that transition times between wells mainly depend upon fluctuations near the saddle point

common scaling patterns in intertrade times of u s stocks we analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the u s economy over a period of 4 yrs for all companies we find that i the probability density function of intertrade times may be fit by a weibull distribution ii when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form iii the intertrade times exhibit power law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales in agreement with the correlation behavior of the absolute price returns for the corresponding company and iv the magnitude series of intertrade time increments is characterized by long range power law correlations suggesting the presence of nonlinear features in the trading dynamics while the sign series is anticorrelated at small scales our results suggest that independent of industry sector market capitalization and average level of trading activity the series of intertrade times exhibit possibly universal scaling patterns which may relate to a common mechanism underlying the trading dynamics of diverse companies further our observation of long range power law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock support the hypothesis that the dynamics of transaction times may play a role in the process of price formation

resonant activation in a bistable system the analog simulation of an overdamped brownian particle in a quartic double well potential driven by an external either gaussian or dichotomic multiplicative noise is performed with special focus on the phenomenon of resonant activation such an effect is shown to occur on increasing the correlation time of the multiplicative noise while keeping the noise variance constant the asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated simple qualitative arguments are produced to justify the results thus obtained furthermore the traversal barrier that is the effective barrier at the time the system switches state is shown to have a minimum for a certain value of the noise correlation time though not always in coincidence with the relevant resonant activation value textcopyright 1996 the american physical society

calibration of the subdiffusive arithmetic brownian motion with tempered stable waiting times in the classical analysis many models used to real data description are based on the standard brownian diffusion type processes however some real data exhibit characteristic periods of constant values in such cases the popular systems seem not to be applicable therefore we propose an alternative approach based on the combination of the popular brownian motion with drift called also the arithmetic brownian motion and tempered stable subordinator the probability density function of the proposed model can be described by a fokker planck type equation and therefore it has many similar properties as the popular brownian motion with drift in this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic brownian motion and calibrate the analyzed process to the real financial data

generalized fokker planck equation for non markovian processes this paper deals with a system of linear non markovian langevin equations with memory functions that are not constant in time and a nonzero initial instant of time a set of statistical means based on the application of a generalized furutsu novikov formula was used to derive a generalized fokker planck equation corresponding to this system and holding for both long and short instants of time considered as an example is the brownian motion of a particle in a viscoelastic fluid with a particular relaxation time

tempered stable levy motion driven by stable subordinator a b s t r a c t in this article we propose a new model for financial data description combining two independent mechanisms namely the tempered stable process and inverse stable subordinator we obtain a new model which captures not only the tempered stable character of the underlying data but also such a property as periods in which the values of an asset stay on the same level moreover we classify our system to the family of subdiffusive processes and investigate its tail behavior we describe in detail testing and estimation procedures for the proposed model in the last step we calibrate our model to the real data

on a nonclassical problem for some quasilinear hyperbolic equation u 0 t bu l t 0itit 1 3 here t is a positive continuous function on 0 t 0 b 0 p 1 0 and l are real constants equations of type 1 1 arise e g in gas dynamics 10 13 while 1 2 1 3 is a generalization of periodic boundary conditions our aim is to 1nd all global solutions to problem 1 1 1 3 note that the boundary conditions are consistent and may admit several solutions

fokker planck type equations associated with fractional brownian motion controlled by infinitely divisible processes abstract in this paper we study the anomalous diffusion process driven by fractional brownian motion delayed by general infinitely divisible subordinator we show the analyzed process is the stochastic representation of the fokker planck type equation that describes the probability density function of an introduced model moreover we study main characteristics of the examined process the first two moments that allow us in special cases for classification of it as a system with accelerating subdiffusion property

generalization of the classical kramers rate for non markovian open systems out of equilibrium we analyze the behavior of a brownian particle moving in a double well potential the escape probability of this particle over the potential barrier from a metastable state toward another state is known as the kramers problem in this work we generalize kramers rate theory to the case of an environment always out of thermodynamic equilibrium reckoning with non markovian effects

quasicrystalline ground states without matching rules a simple local cluster interaction is presented which has as only ground states perfectly quasicrystalline tilings from a single local isomorphism class since these tilings do not allow for any perfect matching rules it is thereby shown that the class of structures which are the ground state of some finite range interaction is considerably larger than previously anticipated cluster interactions having a quasicrystalline ground state turn out to be simple and robust and therefore provide an attractive explanation for the existence of quasicrystals a simplified version of our cluster interaction is found to have super tile random tiling ground states due to the large size of the super tiles these random tilings still look perfect on a local scale

option pricing in subdiffusive bachelier model the earliest model of stock prices based on brownian diffusion is the bachelier model in this paper we propose an extension of the bachelier model which reflects the subdiffusive nature of the underlying asset dynamics the subdiffusive property is manifested by the random infinitely divisible periods of time during which the asset price does not change we introduce a subdiffusive arithmetic brownian motion as a model of stock prices with such characteristics the structure of this process agrees with two stage scenario underlying the anomalous diffusion mechanism in which trapping random events are superimposed on the langevin dynamics we find the corresponding fractional fokker planck equation governing the probability density function of the introduced process we construct the corresponding martingale measure and show that the model is incomplete we derive the formulas for european put and call option prices we describe explicit algorithms and present some monte carlo simulations for the particular cases of stable and tempered stable distributions of waiting times

subordinated α stable ornstein uhlenbeck process as a tool for financial data description abstract the classical financial models are based on the standard brownian diffusion type processes however in the exhibition of some real market data like interest or exchange rates we observe characteristic periods of constant values moreover in the case of financial data the assumption of normality is often unsatisfied in such cases the popular vasicek model that is a mathematical system describing the evolution of interest rates based on the ornstein uhlenbeck process seems not to be applicable therefore we propose an alternative approach based on a combination of the popular ornstein uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior the probability density function of the proposed process can be described by a fokker planck type equation and therefore it can be examined as an extension of the basic ornstein uhlenbeck model in this paper we propose the parameters estimation method and calibrate the subordinated vasicek model to the interest rate data

fractional fokker planck equation with tempered α stable waiting times langevin picture and computer simulation in this paper we introduce a langevin type model of subdiffusion with tempered stable waiting times we consider the case of space dependent external force fields the model displays subdiffusive behavior for small times and it converges to standard gaussian diffusion for large time scales we derive general properties of tempered anomalous diffusion from the theory of tempered stable processes in particular we find the form of the fractional fokker planck equation corresponding to the tempered subdiffusion we also construct an algorithm of simulation of sample paths of the introduced process we apply the algorithm to approximate solutions of the fractional fokker planck equation and to study statistical properties of the tempered subdiffusion via monte carlo methods

anomalous diffusion testing ergodicity breaking in experimental data recent advances in single molecule experiments show that various complex systems display nonergodic behavior in this paper we show how to test ergodicity and ergodicity breaking in experimental data exploiting the so called dynamical functional we introduce a simple test which allows us to verify ergodic properties of a real life process the test can be applied to a large family of stationary infinitely divisible processes we check the performance of the test for various simulated processes and apply it to experimental data describing the motion of mrna molecules inside live escherichia coli cells we show that the data satisfy necessary conditions for mixing and ergodicity the detailed analysis is presented in the supplementary material

non markovian effects on the brownian motion of a free particle abstract non markovian effects on the brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated under the framework of generalized fokker planck equations rayleigh and smoluchowski equations more specifically it is predicted that non markovian features can diminish the values of both the root mean square displacement and the root mean square momentum thereby assuring the mathematical property of analyticity of such physically observable quantities for all times t 0 accordingly the physical concept of non markovian brownian trajectory turns out to be mathematically well defined by differentiable functions for all t 0 another consequence of the non markovicity property is that the langevin stochastic equations underlying the fokker planck equations should be interpreted as genuine differential equations and not as integral equations according to a determined interpretation rule doob s rule for instance

langevin picture of subdiffusion with infinitely divisible waiting times in this paper we study a langevin approach to modeling of subdiffusion in the presence of time dependent external forces we construct a subordinated langevin process whose probability density function solves the subdiffusive fractional fokker planck equation we generalize the results known for the levy stable waiting times to the case of infinitely divisible waiting time distributions our approach provides a complete mathematical description of subdiffusion with time dependent forces moreover it allows to study the trajectories of the constructed process both analytically and numerically via monte carlo methodology

on fractional tempered stable processes and their governing differential equations we derive the governing equation of the tempered stable subordinator hereafter tss which generalizes the space fractional differential equation satisfied by the law of the stable subordinator itself this equation is expressed in terms of the shifted fractional derivative of order 0 1 coinciding with the stability parameter we then generalize this equation by introducing a time fractional derivative of order 0 1 resp 1 1 and we prove that it is satisfied by the law of a tss time changed by the inverse of a stable subordinator resp by the stable subordinator itself the corresponding processes can therefore be called fractional ts processes finally we provide fractional extensions of the relativistic stable processes which we define as a brownian motion with a random time argument represented by independent fractional ts processes of order resp 1

existence and uniqueness of periodic solutions for higher order hyperbolic partial differential equations abstract assuming the smoothness and a generalized lipschitz condition we establish the existence and uniqueness of the periodic solutions of higher order nonlinear hyperbolic partial differential equations

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

an alternative view on quasicrystalline random tilings we apply a framework for the description of random tilings without height representation which was proposed recently to the special case of quasicrystalline random tilings two important examples are discussed thereby demonstrating the consistency of this alternative description with the conventional one we also clarify the latter by deriving a group theoretic criterion for the validity of the first random tiling hypothesis

random tilings of high symmetry i mean field theory we study random tiling models in the limit of high rotational symmetry in this limit a mean field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions we base our mean field theory on an iterative tiling construction inspired by the work of de bruijn in addition to the entropy we consider correlation functions phason elasticity and the thermodynamic limit tilings of dimension other than two are considered briefly

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

exact solution of an octagonal random tiling model we consider the two dimensional random tiling model introduced by cockayne i e the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons at the appropriate relative densities the correlations have eightfold rotational symmetry we reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles the partition function of this model can be calculated by diagonalizing a transfer matrix using the bethe ansatz ba the ba equations can be solved providing exact values of the entropy and elastic constants

the vallee poussin problem for higher order nonlinear hyperbolic equations for higher order nonlinear hyperbolic equations nonclassical boundary value problems of vallee poussin type are studied and unimprovable in a sense sufficient conditions of solvability unique solvability and well posedness are established