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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 3, Pages 534–556 (Mi tvp2447)  

Disorder Problem for Poisson Process in Generalized Bayesian Setting

E. V. Burnaev

Moscow Institute of Physics and Technology

Abstract: This paper deals with the quickest detection of a change of the intensity of the Poisson process. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the conditional-extremal optimal stopping problem for a piecewise-deterministic Markov process. The optimal procedure for the disorder problem is obtained and asymptotics of the Bayesian risk function is calculated.

Keywords: disorder, Poisson process, optimal stopping, differential-difference equation, free-boundary problem, continuous-fit condition, smooth-fit condition, Bayesian risk.

DOI: https://doi.org/10.4213/tvp2447

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English version:
Theory of Probability and its Applications, 2009, 53:3, 500–518

Bibliographic databases:

Received: 13.08.2007
Revised: 02.02.2008

Citation: E. V. Burnaev, “Disorder Problem for Poisson Process in Generalized Bayesian Setting”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 534–556; Theory Probab. Appl., 53:3 (2009), 500–518

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