Analytically measurable selection of epsilon optimal transition kernals

Abstract

The problem of existence of ah ε-optimal transition kernel for a canonical continuous time stochastic process with a general cost variable is considered. An analytically measurable, ε-optimal kernel exists if the state space is a compact Banach space, the cost variable is lower-semi-analytic, and the graph of the admissibility function is an analytic set. The result is applied to a problem in which the controller is to optimally select transition probabilities for a non-Markovian step process based on statistical estimates of holding time distributions.