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On adaptive control of Markov processes. (English) Zbl 0639.60049

This paper extends the results of the first author’s previous work, Probability theory, Warsaw 1976, Banach Cent. Publ. 5, 159-175 (1979; Zbl 0439.60069), to the continuous-time case. A sufficient condition to ensure the existence of an optimal stationary strategy to control a countable Markov process is given. The asymptotic behaviour of the criterion functional is investigated. An example is given.
Reviewer: M.Tibaldi

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
93E20 Optimal stochastic control

Citations:

Zbl 0439.60069
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References:

[1] B. M. Brown: Martingale Central Limit Theorems. Ann. Math. Statist. 42 (1971), 59-66. · Zbl 0218.60048
[2] A. Hordijk: Dynamic Programming and Markov Potential Theory. Math. Centrum, Amsterdam 1974. · Zbl 0284.49012
[3] P. Mandl: On the adaptive control of countable Markov chains. Prob. Theory, Banach Center Publications, Vol. 5, 159-173, Warsaw 1979. · Zbl 0439.60069
[4] P. Mandl: Martingale Methods in Discrete State Random Processes. Supplement to the Journal Kybernetika 18 (1982).
[5] M. R. Romera: Adaptive Control of Markov Processes with Countable State Space. Doctoral Thesis (in Spanish). Universidad Complutense, Madrid 1985.
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