An approximation scheme for quasi-stationary distributions of killed diffusions

Andi Q. Wang, Gareth O. Roberts and David Steinsaltz

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 3193-3219

Abstract: In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasi-stationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasi-stationary Monte Carlo method for sampling from Bayesian posterior distributions.

Keywords: Asymptotic pseudo-trajectory; Killed diffusion; Quasi-stationary distribution; Quasi-stationary Monte Carlo method; Stochastic approximation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.09.010

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