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Эта публикация цитируется в 21 научных статьях (всего в 21 статьях)
Convergence of probability measures and Markov decision models with incomplete information
Eugene A. Feinberga, Pavlo O. Kasyanovb, Michael Z. Zgurovskyb a Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA
b Institute for Applied System Analysis, National Technical University of Ukraine "Kyiv Polytechnic Institute", Kyiv, Ukraine
Аннотация:
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise convergence, and convergence in total variation. First, it describes and compares necessary and sufficient conditions for these types of convergence, some of which are well-known, in terms of convergence of probabilities of open and closed sets and, for the probabilities on the real line, in terms of convergence of distribution functions. Second, it provides criteria for weak and setwise convergence of probability measures and continuity of stochastic kernels in terms of convergence of probabilities defined on the base of the topology generated by the metric. Third, it provides applications to control of partially observable Markov decision processes and, in particular, to Markov decision models with incomplete information.
Поступило в июне 2014 г.
Образец цитирования:
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky, “Convergence of probability measures and Markov decision models with incomplete information”, Стохастическое исчисление, мартингалы и их применения, Сборник статей. К 80-летию со дня рождения академика Альберта Николаевича Ширяева, Труды МИАН, 287, МАИК «Наука/Интерпериодика», М., 2014, 103–124; Proc. Steklov Inst. Math., 287:1 (2014), 96–117
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tm3583https://doi.org/10.1134/S0371968514040062 https://www.mathnet.ru/rus/tm/v287/p103
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Страница аннотации: | 202 | PDF полного текста: | 63 | Список литературы: | 40 |
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