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

Michel Benaïm; Nicolas Champagnat; Denis Villemonais

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arXiv · 1904.08620

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

Michel Benaïm·Nicolas Champagnat·Denis Villemonais

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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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Michel Benaïm, Nicolas Champagnat, Denis Villemonais. 2021-02-15. Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain. https://arxiv.org/abs/1904.08620

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