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Estimation and control in Markov chains

Published online by Cambridge University Press:  01 July 2016

P. Mandl
P. Mandl*
Affiliation:
Institute of Information Theory and Automation, Czechoslovak Academy of Sciences
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Abstract

We consider a finite controlled Markov chain, the description of which depends on an unknown parameter a, and investigate the following control policy. To each a an optimal stationary control is associated. a is estimated recurrently from the trajectory by the minimum contrast method, and the optimal stationary control corresponding to the estimate is used. We present asymptotic properties of the estimate and of the criterion function. They follow from the law of large numbers and from the central limit theorem for controlled Markov chains derived with the aid of martingales.

Keywords

CONTROLLED MARKOV CHAINSASYMPTOTIC BEHAVIOURUNKNOWN PARAMETERSMINIMUM CONTRAST ESTIMATESCONTROLS BASED ON ESTIMATES
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 40 - 60
Copyright
Copyright © Applied Probability Trust 1974 

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