An Approximation Scheme for Quasistationary Distributions of Killed Diffusions
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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 also killed at a given rate and 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 quasistationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasistationary Monte Carlo method for sampling from Bayesian posterior distributions in large data settings.
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