An approximation scheme for quasi-stationary distributions of killed diffusions
| Autor: | Andi Q. Wang, Gareth O. Roberts, David Steinsaltz |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Applied Mathematics 010102 general mathematics Monte Carlo method Bayesian probability Probability (math.PR) Sampling (statistics) Stochastic approximation 01 natural sciences Measure (mathematics) Methodology (stat.ME) 010104 statistics & probability 60B12 60J60 37C50 (Primary) 65C05 (Secondary) Distribution (mathematics) Diffusion process Modeling and Simulation FOS: Mathematics Applied mathematics Almost surely 0101 mathematics Mathematics - Probability Statistics - Methodology Mathematics |
| Zdroj: | Stochastic Processes and their Applications. |
| ISSN: | 0304-4149 |
| Popis: | 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. Comment: v2: revised version, 29 pages, 1 figure |
| Databáze: | OpenAIRE |
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