A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations
成果类型：
Article
署名作者：
Yakir, B; Pollak, M
署名单位：
Hebrew University of Jerusalem
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1998
页码：
749-774
关键词：
摘要：
The probability that a stochastic process with negative drift exceed a value a often has a renewal-theoretic approximation as a --> infinity. Except for a process of iid random variables, this approximation involves a constant which is not amenable to analytic calculation. Naive simulation of this constant has the drawback of necessitating a choice of finite a, thereby hurting assessment of the precision of a Monte Carlo simulation estimate, as the effect of the discrepancy between a and infinity is usually difficult to evaluate. Here we suggest a new way of representing the constant. Our approach enables simulation of the constant with prescribed accuracy. We exemplify our approach by working out the details of a sequential power one hypothesis testing problem of whether a sequence of observations is lid standard normal against the alternative that the sequence is AR(1). Monte Carlo results are reported.