Related papers: Limit theorems for random processes with random ti…

Let $\{X_n;n\ge 1\}$ be a sequence of independent random variables on a probability space $(\Omega, \mathcal{F}, P)$ and $S_n=\sum_{k=1}^n X_k$. It is well-known that the almost sure convergence, the convergence in probability and the…

In this paper we establish functional Erd\H{o}s-Renyi laws for L\'evy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework,…

In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some…

We study the asymptotics of a Markovian system of $N \geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random…

We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…

We prove a quenched local central limit theorem for continuous-time random walks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian…

We provide an original and general sufficient criterion ensuring the exponential contraction of Feynman-Kac semi-groups of penalized processes. This criterion is applied to time-inhomogeneous one-dimensional diffusion processes conditioned…

We give bounds on the rate of convergence to equilibrium of the symmetric simple exclusion process in $\Z^d$. Our results include the existent results in the literature. We get better bounds and larger class of initial states via a unified…

We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on $\mathbb{Z}^d$. We assume that the transition probabilities of the walk depend not too strongly on the environment and…

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems.

In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover,…

We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…

Many applications in networked control require intermittent access of a controller to a system, as in event-triggered systems or information constrained control applications. Motivated by such applications and extending previous work on…

In this note we give necessary and sufficient conditions for the validity of the local spectral convergence, in balls, on the $RCD^*$-setting.

Let $(X_n \colon n\in\Z)$ be a two-sided recurrent Markov chain with fixed initial state $X_0$ and let $\nu$ be a probability measure on its state space. We give a necessary and sufficient criterion for the existence of a non-randomized…

Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, a functional limit…

For linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, we study functional convergence of the joint partial sum and partial maxima processes. We derive a…

We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct…