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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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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Dates et versions

hal-02101739 , version 1 (17-04-2019)
hal-02101739 , version 2 (14-07-2020)
hal-02101739 , version 3 (15-02-2021)

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Michel Benaïm, Nicolas Champagnat, Denis Villemonais. Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain. 2020. ⟨hal-02101739v2⟩

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