In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a...

In some recent papers, some procedures based on some weighted empirical measures related to decreasing-step Euler schemes have been investigated to approximate the stationary regime of a diffusion (possibly with jumps) for a class of functionals of the process. This method is efficient but needs...

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific...

We consider a sequence ([xi]n)n=1 of i.i.d. random values residing in the domain of attraction of an extreme value distribution. For such a sequence, there exist (an) and (bn), with an0 and for every n=1, such that the sequence (Xn) defined by Xn=(max([xi]1,...,[xi]n)-bn)/an converges in...

We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a Lévy process. The main interest of this work is to compare the rates induced by "exact" and "approximate"...

Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links...

Let (L[theta])[theta][epsilon]N be a family of elliptic diffusion operators on a compact and connected smooth manifold M, whose terms of first order are indexed by a parameter [theta] living in N, the n-dimensional torus. For each fixed [theta], we associate to L[theta] its invariant probability...

We consider the simulated annealing algorithm associated to a potential U on a graph (M, q) (reversible or satisfying the Hajek's weak reversibility condition), whose temperature at time t [greater-or-equal, slanted] 0 is given by k ln-1 (1 + t), with k c(M, U) the critical constant for the...