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An approximation scheme for quasi-stationary distributions of killed diffusions

Author

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

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.

Suggested Citation

  • Wang, Andi Q. & Roberts, Gareth O. & Steinsaltz, David, 2020. "An approximation scheme for quasi-stationary distributions of killed diffusions," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3193-3219.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:3193-3219
    DOI: 10.1016/j.spa.2019.09.010
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