Related papers: Functional limit theorems for random walks perturb…

Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…

We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant…

This note is a companion article to the recent paper L\"ocherbach, Loukianova, Marini (2024). We consider mean field systems of interacting particles. Each particle jumps with a jump rate depending on its position. When jumping, a…

We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or vertex) visited to increase the frequency of return visits.…

Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…

We investigate the stochastic motion of a Brownian particle in the harmonic potential with a time-dependent force constant. It may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a…

For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…

We examine two analytical characterisation of the metastable behavior of a Markov chain. The first one expressed in terms of its transition probabilities, and the second one in terms of its large deviations rate functional. Consider a…

In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…

A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random…

We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…

Let $(M_{n},S_{n})_{n\ge 0}$ be a Markov random walk with positive recurrent driving chain $(M_{n})_{n\ge 0}$ having countable state space $\mathcal{S}$ and stationary distribution $\pi$. It is shown in this note that, if the dual sequence…

We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between $+\infty$ and $-\infty$. The conditions are based on a Markov chain which only consists of jumps (overshoots) of…

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy…

We consider stochastic processes on complete, locally compact tree-like metric spaces $(T,r)$ on their "natural scale" with boundedly finite speed measure $\nu$. Given a triple $(T,r,\nu)$ such a speed-$\nu$ motion on $(T,r)$ can be…

Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…

In this paper, we study the stochastic homogenization for a class of symmetric random walks in random conductance model, whose one-step transition probability from $x$ to $y$ is proportional to $|x-y|^{-d-2}$. As the associated jumping…

Let $X_1, X_2, \ldots$ be a sequence of i.i.d. real-valued random variables with mean zero, and consider the scaled random walk of the form $Y^N_{k+1} = Y^N_{k} + a_N(Y^N_k) X_{k+1}$, where $a_N: \mathbb R \to \mathbb R_+$. We show, under…

Motivated by various applications, we describe the scaling limits of bivariate Markov chains $(X,J)$ on $\mathbb Z_+ \times \{1,\ldots,\kappa\}$ where $X$ can be viewed as a position marginal and $\{1,\ldots,\kappa\}$ is a set of $\kappa$…

There is an extensive theory of weak convergence for moving averages and continuous-time random walks (CTRWs) with respect to Skorokhod's M1 and J1 topologies. Here we address the fundamental question of how this translates into functional…