An asymptotic analysis of controlled diffusions with rapidly oscillating parameters
- 1 February 1993
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 42 (2) , 67-92
- https://doi.org/10.1080/17442509308833811
Abstract
This paper presents an asymptotic analysis of controlled diffusions couled by a parameter process. The oscillation rate of the parameter process is assumed to be very large. This gives rise to a limiting problem in which the stochastic parameter process can be replaced by its averaged value. A control for the original problem can be constructed from the optimal control of the limiting problem in a way which guarantees its asymptotic optimality. It is shown that the value function of the original problem converges to the value function of the limiting problem. The convergence rate of the value function and the error estimate of the constructed asymptotically optimal control are obtained. Finally, the results are applied to an adaptive control problem.Keywords
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