Open Access
November 2017 Convergence rate of the powers of an operator. Applications to stochastic systems
Bernard Delyon
Bernoulli 23(4A): 2129-2180 (November 2017). DOI: 10.3150/15-BEJ778

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.

Citation

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Bernard Delyon. "Convergence rate of the powers of an operator. Applications to stochastic systems." Bernoulli 23 (4A) 2129 - 2180, November 2017. https://doi.org/10.3150/15-BEJ778

Information

Received: 1 May 2014; Revised: 1 August 2015; Published: November 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06778239
MathSciNet: MR3648028
Digital Object Identifier: 10.3150/15-BEJ778

Keywords: Markov chains

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 4A • November 2017
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