Related papers: On subordinate random walks

Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…

Let $V$ be a two sided random walk and let $X$ denote a real valued diffusion process with generator ${1/2}e^{V([x])}\frac{d}{dx}(e^{-V([x])}\frac{d}{dx})$. This process is known to be the continuous equivalent of the one dimensional random…

We consider random walks and L\'evy processes in a homogeneous group $G$. For all $p > 0$, we completely characterise (almost) all $G$-valued L\'evy processes whose sample paths have finite $p$-variation, and give sufficient conditions…

Given a random walk $(S_n)$ with typical step distributed according to some fixed law and a fixed parameter $p \in (0,1)$, the associated positively step-reinforced random walk is a discrete-time process which performs at each step, with…

We consider the random walk on a simple point process on $\Bbb{R}^d$, $d\geq2$, whose jump rates decay exponentially in the $\alpha$-power of jump length. The case $\alpha =1$ corresponds to the phonon-induced variable-range hopping in…

We prove an almost sure invariance principle for the capacity and the cardinality of the range of a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d/\alpha > 5/2$, and $d/\alpha >3/2$, respectively. As a…

By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…

In this paper, we work on a class of self-interacting nearest neighbor random walks, introduced in [Probab. Theory Related Fields 154 (2012) 149-163], for which there is competition between repulsion of neighboring edges and attraction of…

Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…

Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…

A random walk with counterbalanced steps is a process of partial sums $\check S(n)=\check X_1+ \cdots + \check X_n$ whose steps $\check X_n$ are given recursively as follows. For each $n\geq 2$, with a fixed probability $p$, $\check X_n$ is…

Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…

This article investigates the behavior of the continuous-time simple random walk on $\mathbb{Z}^d$, $d \geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a…

When it comes to random walk on the integers $\mathbb{Z}$, the arguably first step of generalization beyond simple random walk is the class of one-sidedly continuous random walk, where the stepsize in only one direction is bounded by 1.…

We prove several results on the behavior near t=0 of $Y_t^{-t}$ for certain $(0,\infty)$-valued stochastic processes $(Y_t)_{t>0}$. In particular, we show for L\'{e}vy subordinators that the Pareto law on $[1,\infty)$ is the only possible…

We study models of continuous time, symmetric, $\Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We…

We define a random walk on the set of primitive points of $\mathbb{Z}^d$. We prove that for walks generated by measures satisfying mild conditions these walks are recurrent in a strong sense. That is, we show that the associated Markov…