Related papers: Simulation of the continuous-time random walk usin…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
In this paper the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
We consider a random walk $S_{\tau}$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
A class of discrete time random walks has recently been introduced to provide a stochastic process based numerical scheme for solving fractional order partial differential equations, including the fractional subdiffusion equation. Here we…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
The study of animal movement is challenging because it is a process modulated by many factors acting at different spatial and temporal scales. Several models have been proposed which differ primarily in the temporal conceptualization,…
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…