Geodesic
Some criterions of ``truncatedness'' of the optimal stopping moment in sequential analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 601-613

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We consider the following question: when in the problems of sequential analysis there exists such a finite $N$ that $\nu\le N$ with probability 1 where $\nu$ is the optimal stopping moment. Our criterions of truncatedness (theorem 1) generalize the results of S. N. Ray [1]. 
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     author = {B. I. Grigelionis and A. N. Shiryaev},
     title = {Some criterions of ``truncatedness'' of the optimal stopping moment in sequential analysis},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a0/}
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B. I. Grigelionis; A. N. Shiryaev. Some criterions of ``truncatedness'' of the optimal stopping moment in sequential analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 601-613. http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a0/