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arXiv · 1808.07086

An approximation scheme for quasi-stationary distributions of killed diffusions

Andi Q. Wang·Gareth O. Roberts·David Steinsaltz
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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.

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Andi Q. Wang, Gareth O. Roberts, David Steinsaltz. 2018-08-21. An approximation scheme for quasi-stationary distributions of killed diffusions. https://doi.org/10.1016/j.spa.2019.09.010

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