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May 2021 Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain
Michel Benaïm, Nicolas Champagnat, Denis Villemonais
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Ann. Inst. H. Poincaré Probab. Statist. 57(2): 726-739 (May 2021). DOI: 10.1214/20-AIHP1093

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.

Nous étudions un processus stochastique avec renforcement, qui évolue suivant une diffusion dans un domaine borné, avec ré-échantillonnage suivant sa mesure d’occupation lorsqu’il atteint la frontière. Nous montrons que sa mesure d’occupation converge vers l’unique distribution quasi-stationnaire de la diffusion absorbée au bord du domaine. Nos preuves s’appuient sur des résultats récents en théorie des distributions quasi-stationnaires et sur des techniques d’approximation stochastique.

Citation

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Michel Benaïm. Nicolas Champagnat. Denis Villemonais. "Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain." Ann. Inst. H. Poincaré Probab. Statist. 57 (2) 726 - 739, May 2021. https://doi.org/10.1214/20-AIHP1093

Information

Received: 17 April 2019; Revised: 1 July 2020; Accepted: 29 July 2020; Published: May 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AIHP1093

Subjects:
Primary: 60B10, 60B12, 60F99, 60J60
Secondary: 60J70

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 2 • May 2021
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