## Random walk in a stratified medium

We study the recurrence properties of a random walk in a stratified medium.

We study the recurrence properties of a random walk in a stratified medium.

The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all copies of files stored on it are lost. They can be retrieved afterwards if copies of the same files are stored on s...

A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the resu...

We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the Cole-Hopf transform. To perform these constructions, we adapt the ...

For general dimension $d$, we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. More precisely, we show that, after blow-up at the scale corresponding to the interparticle distance, the value of the energy in any large enough set is complete...

We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relaxed regularity assumptions on the parameters. We show that such stochastic equations arise within the moder...

The goal of this paper is the presentation of a post-processing method allowing to remove impulse noise in binary images, while preserving thin structures. We use a grain filter as in [5]. We propose a method to automatically determine the required threshold using Galton-Watson processes. We present numerical results and a complete analysis on a sy...

We consider a supercritical branching random walk on R. The consistent maximal displacement is the smallest of the distances between the trajectories of individuals at the nth generation and the boundary of the process. It has been proved by Fang and Zeitouni [7] and by Faraud, Hu and Shi [8] that the consistent maximal displacement grows almost su...

Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong ratio limit theorem for aperiodic random walks on Z^d .

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