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Strongly consistent estimation in a controlled Markov renewal model

Published online by Cambridge University Press:  14 July 2016

Michael Kolonko
Michael Kolonko*
Affiliation:
Universität Karlsruhe
*
∗Postal address: Institut für Mathematische Statistik, Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe, W. Germany.
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Abstract

The optimal control of dynamic models which are not completely known to the controller often requires some kind of estimation of the unknown parameters. We present conditions under which a minimum contrast estimator will be strongly consistent independently of the control used. This kind of estimator is appropriate for the adaptive or ‘estimation and control' approach in dynamic programming under uncertainty. We consider a countable-state Markov renewal model and we impose bounding and recurrence conditions of the so-called Liapunov type.

Keywords

DYNAMIC PROGRAMMINGADAPTIVE CONTROLESTIMATION AND CONTROLESTIMATION IN A MARKOV MODELWAITING LINE WITH UNKNOWN PARAMETERS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 532 - 545
Copyright
Copyright © Applied Probability Trust 1982 

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