Stochastic approximation of quasi-stationary distributions on compact spaces and applications
Abstract
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ensuring the convergence of this measure to the quasi-stationary distribution of the chain. We then apply this method to the numerical approximation of the quasi-stationary distribution of a diffusion process killed on the boundary of a compact set and to the estimation of the spectral gap of irreducible Markov processes. Finally, the sharpness of the assumptions is illustrated through the study of the algorithm in a non-irreducible setting.
Keywords
Cite
@article{arxiv.1606.06477,
title = {Stochastic approximation of quasi-stationary distributions on compact spaces and applications},
author = {Michel Benaim and Bertrand Cloez and Fabien Panloup},
journal= {arXiv preprint arXiv:1606.06477},
year = {2017}
}