Infinite Horizon Risk Sensitive Control of Discrete Time Markov Processes under Minorization Property

Abstract

Risk sensitive control of Markov processes satisfying the minorization property is studied using splitting techniques. Existence of solutions to the multiplicative Poisson equation is shown. Approximation by uniformly ergodic controlled Markov processes is introduced, which allows us to show the existence of solutions to the infinite horizon risk sensitive Bellman equation.