Related papers: Limit theorems for decoupled renewal processes

We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

We introduce and study here a renewal process defined by means of a time-fractional relaxation equation with derivative order $\alpha(t)$ varying with time $t\geq0$. In particular, we use the operator introduced by Scarpi in the Seventies…

The stratified resampling mechanism is one of the resampling schemes commonly used in the resampling steps of particle filters. In the present paper, we prove a central limit theorem for this mechanism under the assumption that the initial…

Let $(X_1, \xi_1), (X_2,\xi_2),\ldots$ be i.i.d.~copies of a pair $(X,\xi)$ where $X$ is a random process with paths in the Skorokhod space $D[0,\infty)$ and $\xi$ is a positive random variable. Define $S_k := \xi_1+\ldots+\xi_k$, $k \in…

Let $F$ be a distribution function on $\mathbb{R}$ with $F(0) = 0 $ and density $f$. Let $\tilde{F}$ be the distribution function of $X_1 - X_2$, $X_i\sim F,\, i=1,2,\text{ iid}$. We show that for a critical Hawkes process with displacement…

We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…

A critical branching process $\left\{ Z_{k},k=0,1,2,...\right\} $ in a random environment is considered. A conditional functional limit theorem for the properly scaled process $\left\{ \log Z_{pu},0\leq u<\infty \right\} $ is established…

We study recurrence properties and the validity of the (weak) law of large numbers for (discrete time) processes which, in the simplest case, are obtained from simple symmetric random walk on $\Z$ by modifying the distribution of a step…

Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in i.i.d. random environment, $Z_{r,n}$ be the number of particles in the process at moment $0\leq r\leq n-1$ that have a positive number of descendants in generation…

Consider a continuous time random walk in $\mathbb{Z}$ with independent and exponentially distributed jumps $\pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of…

We consider deterministic random walks on the real line driven by irrational rotations, or equivalently, skew product extensions of a rotation by $\alpha$ where the skewing cocycle is a piecewise constant mean zero function with a jump by…

We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…

We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…

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…

We consider the simple random walk (or P\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers…

We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…

Consider a discrete-time supercritical discounted branching random walk, in which increments at depth $k$ are independent and identically distributed with the same law as $m^{-kH}Y$, where $Y$ has a fixed law, $H>0$, and $m>1$ is the…

In this work we study a natural transition mechanism describing the passage from a quenched (almost sure) regime to an annealed (in average) one, for a symmetric simple random walk on random obstacles on sites having an identical and…

We consider the limit behavior of an excited random walk (ERW), i.e., a random walk whose transition probabilities depend on the number of times the walk has visited to the current state. We prove that an ERW being naturally scaled…