Special Session 23: 

On some smoothening effects of transition semigroups

Szymon Peszat
Jagiellonian University, Cracow
Poland
Co-Author(s):    
Abstract:
\textbf {Szymon Peszat (Institute of Mathematics, Jagiellonian University and Institute of Mathematics, Polish Academy of Sciences), On some smoothening effects of transition semigroups} An important problem in the theory of Markov processes is the uniqueness 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 so-called Bismut-Elworthy-Li formula for diffusions. This formula guarantees the strong Feller property. Later, I recall the classical result of Hawkes for L\`evy 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 L\`evy processes. \end{document}