Related papers: A Central Limit Theorem for Fleming-Viot Particle …
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in…
We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on…
In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…
We consider the Fleming-Viot particle system consisting of $N$ identical particles evolving in $\mathbb{R}_{>0}$ as Brownian motions with constant drift $-1$. Whenever a particle hits $0$, it jumps onto another particle in the interior. It…
In this paper, we establish a version of the central limit theorem for Markov-Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bounded-Lipschitz distance and enjoy a continuous form of the…
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of…
Consider a continuous time Markov chain with rates Q in the state space \Lambda\cup\{0\} with 0 as an absorbing state. In the associated Fleming-Viot process N particles evolve independently in \Lambda with rates Q until one of them…
The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…
We consider the $N$-particle Fleming-Viot process associated to a normally reflected diffusion with soft catalyst killing. The Fleming-Viot multi-colour process is obtained by attaching genetic information to the particles in the…
The purpose of this paper is to extend the investigation of the Fleming-Viot process in discrete space started in a previous work to two specific examples. The first one corresponds to a random walk on the complete graph. Due to its…
The aim of this paper is to develop a particle approximation for the conditional control problem introduced by P.-L. Lions during his lectures at the Coll\`ege de France in November 2016. We focus on a \textit{soft killing} relaxed version…
In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
We consider a branching system consisting of particles moving according to a Markov family in $\Rd$ and undergoing subcritical branching with a constant rate $V>0$. New particles immigrate to the system according to homogeneous space-time…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
We propose a Markov model for the spread of Hepatitis C virus (HCV) among drug users who use injections. We then proceed to an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a non…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
We prove a limit theorem for an integral functional of a Markov process. The Markovian dynamics is characterized by a linear Boltzmann equation modeling a one-dimensional test particle of mass $\lambda^{-1}\gg 1$ in an external periodic…
In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…