Ergodic Control, Bias, and Sensitive Discount Optimality for Markov Diffusion Processes

摘要

This article deals with expected average reward (a.k.a. ergodic reward) and sensitive discount criteria for a general class of Markov diffusion processes. We give conditions under which: (1) average reward optimality and strong -1- discount optimality are equivalent; (2) strong 0-discount optimality implies bias optimality; and (3) bias optimality implies 0-discount optimality. Moreover, under additional hypotheses, (4) bias optimality also implies strong 0-discount optimality. Thus, under previous results that guarantee average and bias optimality, we ensure that strong -1-discount and strong 0-discount optimality hold.