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.
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
\Bibitem{Bur08}
\by E.~V.~Burnaev
\paper Disorder Problem for Poisson Process in Generalized Bayesian Setting
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 3
\pages 534--556
\mathnet{http://mi.mathnet.ru/tvp2447}
\crossref{https://doi.org/10.4213/tvp2447}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2759709}
\zmath{https://zbmath.org/?q=an:05701630}
\transl
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 3
\pages 500--518
\crossref{https://doi.org/10.1137/S0040585X9798378X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000270196500008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69549130643}
Linking options:
https://www.mathnet.ru/eng/tvp2447
https://doi.org/10.4213/tvp2447
https://www.mathnet.ru/eng/tvp/v53/i3/p534
This publication is cited in the following 3 articles:
Ke Zhou, “The extreme climate event change trend forecast in the Huaihe River Basin, China”, Journal of Water and Climate Change, 2024
Xuyuan Han, Zhenya Liu, “The optimal time to buy and hold stock in a reversal”, Int. J Fin Econ, 2023
Hachmi Ben Ameur, Xuyuan Han, Zhenya Liu, Jonathan Peillex, “When did global warming start? A new baseline for carbon budgeting”, Economic Modelling, 116 (2022), 106005
Citation in format AMSBIB
Contact us: