Functional Occupation Measures and Ergodic Cost Problems for Singularly Perturbed Stochastic Systems

摘要

Functional occupation measures are an extension to occupation measures on the path space of the usual definition of occupation measures for stochastic processes. They are used to get limit and approximation theorems for average cost per unit time problems for many types of controlled or uncontrolled random processes. This paper deals with diffusions reflected diffusions, and singularly perturbed controlled diffusions. There are extensions to wide bandwidth noise driven systems and to many other models. The method provides a convenient and powerful way of characterizing the processes associated with the weak limits of the occupation measures and with the sample limits of the average costs per unit time, as the various parameters of the problem go to their limits. The method can be used to get approximate optimality theorems and similar results for processes which are only approximated by jump diffusions and are of interest over a long time period. (KR)