Martingale limit theorem and its application to an ergodic controlled Markov chain. (English) Zbl 0877.93143
Summary: Slightly different sufficient conditions for the martingale limit theorem of Loève (1978) are studied for an adapted sequence of random variables \({X_{i},{\mathcal F}_{i},i\geq 1}\). As an application of this form of the martingale limit theorem, existence of an optimal control for an ergodic controlled Markov chain with long-run average cost criterion is established under a weaker condition than Borkar’s.
MSC:
| 93E20 | Optimal stochastic control |
Keywords:
Martingale limit theorem; Strong law of large numbers for martingales; Controlled Markov chain; Optimal control; Ergodic controlReferences:
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