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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 : Tuesday, June 21, 2016 - 9:36:15 AM
Last modification on : Monday, April 4, 2022 - 3:24:12 PM
Long-term archiving on: : Thursday, September 22, 2016 - 11:30:16 AM

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  • HAL Id : hal-01334603, version 1
  • ARXIV : 1606.06477

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Michel Benaim, Bertrand Cloez, Fabien Panloup. STOCHASTIC APPROXIMATION OF QUASI-STATIONARY DISTRIBUTIONS ON COMPACT SPACES AND APPLICATIONS. 2016. ⟨hal-01334603v1⟩

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