Sequential testing problems for Poisson processes. (English) Zbl 1081.62546

Peskir, G.; Shiryaev, A. N.

Ann. Stat. 28, No. 3, 837-859 (2000).

Summary: 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 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.

MSC:

62L10	Sequential statistical analysis
62C10	Bayesian problems; characterization of Bayes procedures
62M02	Markov processes: hypothesis testing

Keywords:

Sequential testing; Bayes decision rule; Poisson process; SPRT (sequential probability ratio test); optimal stopping; free-boundary differential-difference Stephan problem; principles of continuous and smooth fit; point (counting)(Cox) process; measure of jumps and its compensator; Itô’s formula

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