Dynamic importance sampling for uniformly recurrent Markov chains

• 成果类型: Article
• 署名作者: Dupuis, P; Wang, H
• 署名单位: Brown University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000001016
• 发表日期: 2005
• 页码: 1-38
• 关键词: large deviations theory; monte-carlo; additive processes; Rare events; simulation

摘要

Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested by a large deviation lower bound analysis. Recent work, however, has suggested that such schemes do not work well in many situations. In this paper we consider dynamic importance sampling in the setting of uniformly recurrent Markov chains. By dynamic we mean that in the course of a single simulation, the change of measure can depend on the outcome of the simulation up till that time. Based on a control-theoretic approach to large deviations, the existence of asymptotically optimal dynamic schemes is demonstrated in great generality. The implementation of the dynamic schemes is carried out with the help of a limiting Bellman equation. Numerical examples are presented to contrast the dynamic and standard schemes.