Stability of long run functionals with respect to stationary Markov controls

TL;DR

This paper investigates how long-term functionals like average cost and risk-sensitive measures depend on stationary Markov controls, analyzing convergence under ergodicity and transition probability conditions.

Contribution

It introduces conditions under which long run functionals are stable when Markov controls converge, extending previous results by relaxing ergodicity assumptions.

Findings

Long run functionals depend continuously on Markov controls under certain conditions.

Uniform ergodicity ensures stability of long-term measures.

Results apply to both average cost and risk-sensitive functionals.

Abstract

In the paper we study dependence of long run functionals and limit characteristics assuming that Borel measurable Markov controls converge pointwise. We consider two kinds of functionals: average cost per unit time and long run risk sensitive. We impose uniform ergodicity assumption, which is later is relaxed and suitable convergence of controlled transition probabilities.