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Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 4, Pages 670–686 (Mi tvp417)  

This article is cited in 2 scientific papers (total in 2 papers)

On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis

A. N. Širyaev

Moscow

Abstract: The question of finding Markov sufficient statistics (see definition 3) in the problem of minimisation of the functional (2) is considered. It is supposed that the parameter $\theta$ the random moment at which the density $f_0$ changes to $f_1$ (§ 1–3) or to one of the $f_1,…,f_m$ (§ 5). In the case when the densities $f_0,f_1,…,f_m$ belong to the exponential family and the functional which is minimized is a non-additive one of a special form, we find a finite number of Markov sufficient statistics. Connections between the problem considered and other problems of sequential analysis are also discussed.

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English version:
Theory of Probability and its Applications, 1964, 9:4, 604–618

Bibliographic databases:

Received: 20.03.1964

Citation: A. N. Širyaev, “On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis”, Teor. Veroyatnost. i Primenen., 9:4 (1964), 670–686; Theory Probab. Appl., 9:4 (1964), 604–618

Citation in format AMSBIB
\Bibitem{Shi64}
\by A.~N.~{\v S}iryaev
\paper On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 4
\pages 670--686
\mathnet{http://mi.mathnet.ru/tvp417}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=174143}
\zmath{https://zbmath.org/?q=an:0138.12505}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 4
\pages 604--618
\crossref{https://doi.org/10.1137/1109082}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Ya. Kartashov, M. A. Novoseltseva, “Obnaruzhenie strukturno-parametricheskikh izmenenii v stokhasticheskikh sistemakh v realnom masshtabe vremeni algoritmami nepreryvnykh drobei i strukturnogo analiza”, UBS, 34 (2011), 62–91  mathnet
    2. Yueksel S., “A Tutorial on Quantizer Design for Networked Control Systems: Stabilization and Optimization”, Applied and Computational Mathematics, 10:3 (2011), 365–401  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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