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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01334603
Contributeur : Fabien Panloup <>
Soumis le : lundi 6 novembre 2017 - 22:14:20
Dernière modification le : mardi 20 novembre 2018 - 16:04:29

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BCP_QSD_AAP_revision.pdf
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  • HAL Id : hal-01334603, version 3
  • ARXIV : 1606.06477

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Michel Benaim, Bertrand Cloez, Fabien Panloup. Stochastic approximation of quasi-stationary distributions on compact spaces and applications. 2017. 〈hal-01334603v3〉

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