Convergence rate of the powers of an operator. Applications to stochastic systems

Abstract

We extend the traditional operator theoretic approach for the study of dynamical systems in order to handle the problem of non-geometric convergence. We show that the probabilistic treatment developed and popularized under Richard Tweedie’s impulsion, can be placed into an operator framework in the spirit of Yosida–Kakutani’s approach. General theorems as well as specific results for Markov chains are given. Application examples to general classes of Markov chains and dynamical systems are presented.