A SEQUENTIAL MONTE CARLO APPROACH TO COMPUTING TAIL PROBABILITIES IN STOCHASTIC MODELS

• 成果类型: Article
• 署名作者: Chan, Hock Peng; Lai, Tze Leung
• 署名单位: National University of Singapore; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP758
• 发表日期: 2011
• 页码: 2315-2342
• 关键词: recurrent markov-chains; Large deviations theory; error probabilities; random-walks; approximations; simulation

摘要

Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential Monte Carlo estimators, we show how resampling weights can be chosen to yield logarithmically efficient Monte Carlo estimates of large deviation probabilities for multidimensional Markov random walks.