Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics

Albert N. Shiryaev ()
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Albert N. Shiryaev: Steklov Mathematical Institute of the Russian Academy of Sciences

A chapter in Mathematical Control Theory and Finance, 2008, pp 377-386 from Springer

Abstract: Summary We consider generalized Bayesian “nonlinear delay penalty” problems of the quickest detection of spontaneous appearing of “time-change” point θ ∈ [0, ∞] when the observable process changes its probability characteristics. For some classes of observable processes and penalty functions we describe the structure of the Markov family of “sufficient statistics” that gives a possibility to apply the methods of the general Markovian optimal stopping theory to solving of the quickest detection problems with a “nonlinear delay penalty”.

Keywords: Penalty Function; Independent Increment; Brownian Motion Model; Observable Process; Brownian Model (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69532-5_21

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DOI: 10.1007/978-3-540-69532-5_21

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