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June 2000 Sequential testing problems for Poisson processes
G. Peskir, A. N. Shiryaev
Ann. Statist. 28(3): 837-859 (June 2000). DOI: 10.1214/aos/1015952000

Abstract

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.

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G. Peskir. A. N. Shiryaev. "Sequential testing problems for Poisson processes." Ann. Statist. 28 (3) 837 - 859, June 2000. https://doi.org/10.1214/aos/1015952000

Information

Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1081.62546
MathSciNet: MR1792789
Digital Object Identifier: 10.1214/aos/1015952000

Subjects:
Primary: 60G40 , 62C10 , 62L10
Secondary: 34K10 , 60J75 , 62L15

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

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • June 2000
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