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On controlled one-dimensional diffusion processes with unknown parameter

Published online by Cambridge University Press:  01 July 2016

Věra Dufková
Věra Dufková*
Affiliation:
Institute of Information Theory and Automation, Czechoslovakian Academy of Sciences, Prague
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Abstract

We consider a controlled diffusion process, the description of which depends on an unknown parameter α, and investigate the following control policy. To each α an optimal stationary control is associated. α is estimated recurrently from the trajectory by Bayes' method, and the optimal stationary control corresponding to the estimate is used. We establish the consistency of the estimate, and present asymptotic properties of the criterion function. They follow from the central limit theorem, from the law of large numbers and from the law of the iterated logarithm for local martingales.

Keywords

DIFFUSION PROCESSESASYMPTOTIC BEHAVIOURUNKNOWN PARAMETERLOCAL MARTINGALESOPTIMAL CONTROL

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 1 , March 1977 , pp. 105 - 124
Copyright
Copyright © Applied Probability Trust 1977 

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References

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