Sequential testing problems for Poisson processes
成果类型：
Article
署名作者：
Peskir, G; Shiryaev, AN
署名单位：
Aarhus University; University of Zagreb; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2000
页码：
837-859
关键词：
摘要：
We present the explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the intensity of an observed Poisson process. The method of proof consists of reducing the initial problem to a free-boundary differential-difference Stephan problem and solving the latter by use of the principles of smooth and continuous fit. A rigorous proof of the optimality of the Wald's sequential probability ratio test in the variational formulation of the problem is obtained as a consequence of the solution of the Bayesian problem.