Michel Benaïm, Nicolas Champagnat, Denis Villemonais
Published 2019-04-18Version 1
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.
Diffusion semigroup on manifolds with time-dependent metrics
Fluctuations for the Ginzburg-Landau $\nabla φ$ Interface Model on a Bounded Domain
Sharp $L^q$-Convergence Rate in $p$-Wasserstein Distance for Empirical Measures of Diffusion Processes
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