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van Kieu, Pham
A diffusion approximation in the ruin problem for a controlled Markov chain. (English). Kybernetika, vol. 10 (1974), issue 2, pp. (125)-132
MSC: 60J10, 60J70, 60J99, 90C40, 93E20 | MR 0359034 | Zbl 0281.60071
References:
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[2] P. Billingsley: Convergence of probability measures. New York 1968. MR 0233396 | Zbl 0172.21201
[3] J. Z. Doob: Stochastic processes. New York-London 1953. Zbl 0053.26802
[4] Z. Koutský: Probability of a service-system's ruin in the case of finite initial capital. In: Trans. of Fourth Prague Conf. on Information Th. etc. Prague 1967, 425-434. MR 0232589
[5] P. Mandl: Analytical treatment of one-dimensional Markov processes. Prague-Heidelberg 1968. MR 0247667 | Zbl 0179.47802
[6] P. Mandl: A connection between controlled Markov chain and martingales. Kybernetika 9 (1973), 237-241. MR 0323427
[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. MR 0292573 | Zbl 0234.49020
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