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

In: Mathematical Control Theory and Finance

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  • Albert N. Shiryaev

    (Steklov Mathematical Institute of the Russian Academy of Sciences)

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”.

Suggested Citation

  • Albert N. Shiryaev, 2008. "Generalized Bayesian Nonlinear Quickest Detection Problems: On Markov Family of Sufficient Statistics," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 377-386, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_21
    DOI: 10.1007/978-3-540-69532-5_21
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