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Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain

Michel Benaïm 1 Nicolas Champagnat 2 Denis Villemonais 2
2 BIGS - Biology, genetics and statistics
Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its occupation measure converges to the unique quasi-stationary distribution of the diffusion process absorbed at the boundary of the domain. Our proofs use recent results in the theory of quasi-stationary distributions and stochastic approximation techniques.
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https://hal.archives-ouvertes.fr/hal-02101739
Contributor : Nicolas Champagnat Connect in order to contact the contributor
Submitted on : Monday, February 15, 2021 - 9:54:41 AM
Last modification on : Saturday, October 16, 2021 - 11:18:02 AM

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Michel Benaïm, Nicolas Champagnat, Denis Villemonais. Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2022, 57 (2), pp.726-739. ⟨10.1214/20-AIHP1093⟩. ⟨hal-02101739v3⟩

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