Convergence rate of the powers of an operator. Applications to stochastic systems. (English) Zbl 1407.60096

Delyon, Bernard

Bernoulli 23, No. 4A, 2129-2180 (2017).

Summary: 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.

MSC:

60J05	Discrete-time Markov processes on general state spaces
60B10	Convergence of probability measures

Keywords:

Markov chains