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On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 670-686 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $f_1,\dots,f_m$ (§ 5). In the case when the densities $f_0,f_1,\dots,f_m$ 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. 
@article{TVP_1964_9_4_a6,
     author = {A. N. \v{S}iryaev},
     title = {On {Markov} {Sufficient} {Statistics} in {Nonadditive} {Bayes} {Problems} of {Sequential} {Analysis}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {670--686},
     year = {1964},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a6/}
}
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A. N. Širyaev. On Markov Sufficient Statistics in Nonadditive Bayes Problems of Sequential Analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 670-686. http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a6/