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.
Keywords: Quasi-stationary distribution, interacting particle system, Wasserstein distance, couplings, propagation of chaos
@article{PS_2022__26_1_1_0,
author = {Journel, Lucas and Monmarch\'e, Pierre},
title = {Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: {Uniform} estimates in a compact soft case},
journal = {ESAIM: Probability and Statistics},
pages = {1--25},
year = {2022},
publisher = {EDP-Sciences},
volume = {26},
doi = {10.1051/ps/2021017},
mrnumber = {4363453},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2021017/}
}
TY - JOUR AU - Journel, Lucas AU - Monmarché, Pierre TI - Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case JO - ESAIM: Probability and Statistics PY - 2022 SP - 1 EP - 25 VL - 26 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2021017/ DO - 10.1051/ps/2021017 LA - en ID - PS_2022__26_1_1_0 ER -
%0 Journal Article %A Journel, Lucas %A Monmarché, Pierre %T Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case %J ESAIM: Probability and Statistics %D 2022 %P 1-25 %V 26 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2021017/ %R 10.1051/ps/2021017 %G en %F PS_2022__26_1_1_0
Journel, Lucas; Monmarché, Pierre. Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 1-25. doi: 10.1051/ps/2021017
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