In this paper a stochastic control model is studied that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control that satisfies a Lipschitz condition and is δ-optimal for the limit model remains δ-optimal also in the prelimit model. The method of proof uses the technique of weak convergence of stochastic processes. The result that is obtained extends a previous work by the authors, where the limit model is deterministic.
|Number of pages||28|
|Journal||Theory of Probability and its Applications|
|State||Published - Dec 1999|
- Asymptotic optimality
- Stochastic control
- Stochastic differential equations
- Weak convergence