Related papers: A Semi-Markov Algorithm for Continuous Time Random…
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that…
We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…
We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution…
The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, $P_l$, and waiting-time, $P_t$,…
We present a semi-Markov model of random walk on complex networks in discrete and continuous-time scenario. In the general setting of the semi-Markov chains, the duration of stay at given node - the sojourn time - is random, and the…
This paper studies long range random walks on ${\mathbb{Z}_q}^d$. $X_{t+1} = X_t + Z_t \mod q$, with $(Z_t)$ independent and identically distributed. Multiple entries of $Z_t$ can be non-zero in a transition. An emphasis is on finding the…
Some specific features and extensions of the continuous time random walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR CTRW…
In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…
Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function…
We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…
We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random…
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences.…
The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its corresponding Fokker-Planck equation has space fractional…
We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point…
Aging is a prevalent phenomenon in physics, chemistry and many other fields. In this paper we consider the aging process of uncoupled Continuous Time Random Walk Limits (CTRWL) which are Levy processes time changed by the inverse stable…
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…