PDE Seminar Abstracts

On some smoothing effects of transition semigroups

Szymon Peszat
Jagiellonian University and Institute of Mathematics, Polish Academy of Sciences, Poland
Fri 19th Feb 2016, 11-12am, Carslaw Room 535


An important problem in the theory of Markov processes is the unique- ness of an invariant measure and its ergodicity. This holds if the transition semigroup exhibits some smoothening effects: for example if it is strong Feller and irreducible or asymptotic strong Feller. In the talk I will derive the socalled Bismut-Elworthy-Li formula for diffusions. This formula guarantees the strong Feller property. Later, I recall the classical result of Hawkes for Lévy semigroups. It relates the strong Feller property with absolute continuity of the process. The last part of the talk will be devoted to the absolute continuity of Lévy processes