Importance sampling and the cyclic approach
成果类型：
Article
署名作者：
Juneja, S
署名单位：
Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.49.6.900.10016
发表日期：
2001
页码：
900-912
关键词：
摘要：
The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the probability along the most likely paths to the rare event. Traditionally, insights from large deviations theory are used to identify the distribution emphasizing these most likely paths. In this paper we develop an intuitive cyclic approach for selecting such a distribution. The key idea is to select a distribution under which the event of interest is no longer rare and the probability of occurrence of a cycle in any sample path remains equal to the original probability of that cycle. We show that only an exponentially twisted distribution can satisfy this equiprobable cycle condition. Using this approach we provide an elementary derivation of the asymptotically optimal change of measure for level crossing probability for Markov-additive processes. To demonstrate its ease of use for more complex stochastic systems, we apply it to determine the asymptotically optimal change of measure for estimating buffer overflow probability of a single-server queue subject to server interruptions.