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A diffusion approximation in the ruin problem for a controlled Markov chain. (English) Zbl 0281.60071
MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J99 Markov processes
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References:
[1] R. Bellman: A Markovian decision process. J. of Math. and Mech. 6 (1957), 679-684. · Zbl 0078.34101
[2] P. Billingsley: Convergence of probability measures. New York 1968. · Zbl 0172.21201
[3] J. Z. Doob: Stochastic processes. New York-London 1953. · Zbl 0053.26802
[4] Z. Koutsk√Ĺ: Probability of a service-system’s ruin in the case of finite initial capital. Trans. of Fourth Prague Conf. on Information Th. etc. Prague 1967, 425-434.
[5] P. Mandl: Analytical treatment of one-dimensional Markov processes. Prague-Heidelberg 1968. · Zbl 0179.47802
[6] P. Mandl: A connection between controlled Markov chain and martingales. Kybernetika 9 (1973), 237-241. · Zbl 0265.60060
[7] R. Morton: On the optimal control of stationary diffusion processes with natural boundaries and discounted cost. J. of Appl. Prob. 8 (1971), 561-572. · Zbl 0234.49020 · doi:10.2307/3212179
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