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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.
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https://hal.archives-ouvertes.fr/hal-01334603
Contributor : Fabien Panloup Connect in order to contact the contributor
Submitted on : Monday, December 5, 2016 - 3:44:38 PM
Last modification on : Wednesday, March 23, 2022 - 12:08:25 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 10:07:03 AM

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  • HAL Id : hal-01334603, version 2
  • ARXIV : 1606.06477

Citation

Michel Benaim, Bertrand Cloez, Fabien Panloup. Stochastic approximation of quasi-stationary distributions on compact spaces and applications. 2016. ⟨hal-01334603v2⟩

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