THEORETICAL PROPERTIES OF QUASI-STATIONARY MONTE CARLO METHODS

• 成果类型: Article
• 署名作者: Wang, Andi Q.; Kolb, Martin; Roberts, Gareth O.; Steinsaltz, David
• 署名单位: University of Oxford; University of Paderborn; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1422
• 发表日期: 2019
• 页码: 434-457
• 关键词: stochastic-approximation; CONVERGENCE; BEHAVIOR; SPACES

摘要

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein-Uhlenbeck process with Gaussian quasi-stationary distribution.