On controlled one-dimensional diffusion processes with unknown parameter
- 1 March 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (01) , 105-124
- https://doi.org/10.1017/s0001867800043147
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
This publication has 2 references indexed in Scilit:
- Recent progress in stochastic processes--A surveyIEEE Transactions on Information Theory, 1973
- On the optimal control of stationary diffusion processes with inaccessible boundaries and no discountingJournal of Applied Probability, 1971