Convergence of the Fleming-Viot algorithm: uniform in time estimates in a compact soft case
Résumé
We establish the convergences (with respect to the simulation time $t$ ; the number of particles $N$ ; the timestep $\gamma$) of the Fleming-Viot algorithm 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 ($t\rightarrow \infty$, $N\rightarrow \infty$ or $\gamma\rightarrow 0$) are independent from the two others.