Dissertation

Approach to Markov Operators on Spaces of Measures by means of equicontinuity

The subject of this thesis, ‘Approach to Markov Operators on Spaces of Measures by Means of Equicontinuity’, combines an analytical and probabilistic approach to Markov operators.

Author: Ziemlańska, M.A.
Date: 10 February 2021
Links: Thesis in Leiden University Scholarly Publications

The subject of this thesis, ‘Approach to Markov Operators on Spaces of Measures by Means of Equicontinuity’, combines an analytical and probabilistic approach to Markov operators. We look at Markov operators coming from deterministic dynamical systems and also stochastic processes which come from a probabilistic approach.In the study of Markov operators and Markov semigroups the central problems are to understand the behaviour of the processes and semigroups. Of particular interest is to identify the existence and uniqueness of invariant measures and long term behaviour of the process and dynamical system defined by the associated Markov operator or semigroup. Research on these questions dates back to the works of Andrey Markov, who described a Markov property for chains. A big part of theory for Markov chains can be found in the book by Meyn and Tweedie, who made a big contribution to the theory of Markov chains and gave a noteworthy description of e-chains, which was the...