Joanna Jaroszewska. Cardinal Stefan Wyszynski University, Warsaw. Asymptotic
properties of semigroups of Markov operators and of families of Markov-type ...
Joanna Jaroszewska Cardinal Stefan Wyszynski University, Warsaw
Asymptotic properties of semigroups of Markov operators and of families of Markov-type nonlinear operators I will present my recent work on the semigroups of Markov operators and on the families of Markov-type nonlinear operators acting on measures. I will start with the discussion of the relationships between various asymptotic properties of Markov semigroups such as the asymptotic strong Feller property, the e-property and the asymptotic e-property. Next I will present the criteria for the existence of invariant probability measures and their asymptotic stability, valid for Fellerian as well as non-Fellerian semigroups. Finally I will discuss variants of these results valid for general families of Markov-type nonlinear operators. I will also show some applications to iterated function systems. References [1] Jaroszewska, J. (2013) On asymptotic equicontinuity of Markov transition functions, Stat. Probab. Lett. 83, no. 3, 943–951. [2] Jaroszewska, J. (2013) A note on iterated function systems with discontinuous probabilities, Chaos Solitons Fractals 49, 28–31. [3] Jaroszewska, J. (2013) The asymptotic strong Feller property does not imply the eproperty for Markov-Feller semigroups, arXiv: 1308.4967.
