This seminar will be presented in hybrid mode.  The speaker will deliver his talk remotely.

Title: On the path-continuity of Markov processes

Abstract: Suppose that we are given a general second order integro-differential operator defined merely on a class of test functions, which corresponds to a càdlàg Markov process, e.g. through the martingale problem. The aim is to present a general result which claims that if the class of test functions is rich enough (yet not necessarily a core), and if G is an open domain on which the generator has the local property expressed in a suitable way, then the Markov process has continuous paths when it passes through G. In fact, because the class of test functions is not necessarily a core, the aforementioned result holds for any Markov extension of the operator. The approach is potential theoretic and covers (possibly time-dependent) operators defined on domains in Hilbert spaces or on spaces of measures. This is joint work with L. Beznea and M. Röckner.