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Controlled Markov Chains
Harry Kesten and Frank Spitzer
The Annals of Probability
Vol. 3, No. 1 (Feb., 1975), pp. 32-40
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2959261
Page Count: 9
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We propose a control problem in which we minimize the expected hitting time of a fixed state in an arbitrary Markov chains with countable state space. A Markovian optimal strategy exists in all cases, and the value of this strategy is the unique solution of a nonlinear equation involving the transition function of the Markov chain.
The Annals of Probability © 1975 Institute of Mathematical Statistics