On ergodic control problems for singularly perturbed Markov processes

In this paper ergodic control problems (optimal stopping, impulsive control, and stochastic control for singularly perturbed Feller Markov processes) are studied. As the main result the so-called limit control principle is shown to hold in each case. The results obtained depend on the averaging properties of the perturbed system which follow from the fact that the perturbing process does not depend on either the perturbed process or on the control.

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