Stationary Markov sets
Stationary solutions and forward equations for controlled and singular martingale problems.
Statistical models for analysing criminal careers
Steady state and scaling limit for a traffic congestion model
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...
Steady-state distributions of piecewise Markov processes
Stochastic coalescence.
Stochastic differential equations with boundary conditions driven by a Poisson noise.
Stochastic flows associated to coalescent processes II : stochastic differential equations
Stochastic flows with interaction and measure-valued processes.
Stratonovich stochastic differential equations driven by general semimartingales
Strong law of large numbers for fragmentation processes
In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1≥η>0.
Strong ratio limit theorems for mixing Markov operators
Structural properties and limit behaviour of linear stochastic systems in Hilbert spaces
Sur la positivité de certains opérateurs
Sur le premier problème de Fourier relatif à l'équation intègro-différentielle du processus sophistiqué markovien mixte
Sur les inégalités de Sobolev logarithmiques, I
Sur les inégalités de Sobolev logarithmiques, II
Sur les trajectoires intrinsèques des processus de Markov et le théorème de Shih
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE method...
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time Markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE...