Abstract
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.
Citation
Harry Kesten. Frank Spitzer. "Controlled Markov Chains." Ann. Probab. 3 (1) 32 - 40, February, 1975. https://doi.org/10.1214/aop/1176996445
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