Geodesic
Disorder Problem for Poisson Process in Generalized Bayesian Setting
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 3, pp. 534-556

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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, optimal stopping, differential-difference equation, free-boundary problem, continuous-fit condition, smooth-fit condition, Bayesian risk.
Mots-clés : Poisson process 
@article{TVP_2008_53_3_a6,
     author = {E. V. Burnaev},
     title = {Disorder {Problem} for {Poisson} {Process} in {Generalized} {Bayesian} {Setting}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {534--556},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_3_a6/}
}
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E. V. Burnaev. Disorder Problem for Poisson Process in Generalized Bayesian Setting. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 3, pp. 534-556. http://geodesic.mathdoc.fr/item/TVP_2008_53_3_a6/