Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case

LJLL, Sorbonne Université.
LJLL and LCT, Sorbonne Université.

^* Corresponding author: pierre.monmarche@sorbonne-universite.fr

Received: 8 November 2019
Accepted: 17 December 2021

Abstract

We establish the convergences (with respect to the simulation time t; the number of particles N; the timestep γ) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary distribution of a diffusion on the d-dimensional torus, killed at a smooth rate. In these conditions, quantitative bounds are obtained that, for each parameter (t →∞, N →∞ or γ → 0) are independent from the two others.