Related papers: Weak convergence of positive self-similar Markov p…

We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in $\mathbb{R}^d$, described in terms of a general stochastic evolution equation. In a setting where the state…

Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. This paper provides explicit connections between the $V$-geometric ergodicity of $P$ and that of finite-rank nonnegative sub-Markov kernels $\Pc_k$…

A multitype continuous-state branching process (MCSBP) ${\rm Z}=({\rm Z}_{t})_{t\geq 0}$, is a Markov process with values in $[0,\infty)^{d}$ that satisfies the branching property. Its distribution is characterised by its branching…

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…

The paper is concerned with the weak convergence of $n$-particle processes to deterministic stationary paths as $n\to\infty$. A Mosco type convergence of a class of bilinear forms is introduced. The Mosco type convergence of bilinear forms…

We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones,…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…

In this paper, we obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov processes as time changed multiplicative…

In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism $\psi(\lambda)=\lambda^{1+\alpha}L(1/\lambda)$ where $\alpha\in [0,1]$ and $L$ is slowly varying at $\infty$.…

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…

We provide a condition for f-ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift…

We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit…

We provide explicit conditions, in terms of the transition kernel of its driving particle, for a Markov branching process to admit a scaling limit toward a self-similar growth-fragmentation with negative index. We also derive a scaling…

Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $\pi$. Let $\Psi$ a function on the state space of the chain, with $\alpha$-tails with respect to $\pi$, $\alpha\in (0,2)$. We find sufficient conditions on the…

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of…

We consider the small mass asymptotic (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The friction coefficient is assumed to be vanishing within certain region. We introduce a…

We obtain a new relation between the distributions $\mu_t$ at different times $t\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a…

For a strictly stationary sequence of nonnegative regularly varying random variables $(X_{n})$ we study functional weak convergence of partial maxima processes $M_{n}(t) = \bigvee_{i=1}^{\lfloor nt \rfloor}X_{i},\,t \in [0,1]$ in the space…

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker…