Translator Disclaimer
August 2018 Stochastic approximation of quasi-stationary distributions on compact spaces and applications
Michel Benaim, Bertrand Cloez, Fabien Panloup
Ann. Appl. Probab. 28(4): 2370-2416 (August 2018). DOI: 10.1214/17-AAP1360

Abstract

As a continuation of a recent paper, 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. Finally, the sharpness of the assumptions is illustrated through the study of the algorithm in a nonirreducible setting.

Citation

Download Citation

Michel Benaim. Bertrand Cloez. Fabien Panloup. "Stochastic approximation of quasi-stationary distributions on compact spaces and applications." Ann. Appl. Probab. 28 (4) 2370 - 2416, August 2018. https://doi.org/10.1214/17-AAP1360

Information

Received: 1 December 2016; Revised: 1 September 2017; Published: August 2018
First available in Project Euclid: 9 August 2018

zbMATH: 06974754
MathSciNet: MR3843832
Digital Object Identifier: 10.1214/17-AAP1360

Subjects:
Primary: 60B12, 60J10, 65C20
Secondary: 34F05, 60J20, 60J60

Rights: Copyright © 2018 Institute of Mathematical Statistics

JOURNAL ARTICLE
47 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 4 • August 2018
Back to Top