On the path-continuity of Markov processes
A talk in the Bielefeld Stochastic Afternoon series by
Iulian Cimpean
| Abstract: | This talk will be held via Zoom (for details email stochana(at)math.uni-bielefeld.de). Suppose that we are given a general second order integro-differential operator defined merely on a class of test functions, which corresponds to a cadlag 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 sufficiently rich (yet not necessarily a core), and if G is a domain in the state space 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 a joint work with L. Beznea and M. Roeckner. Within the CRC this talk is associated to the project(s): A5, B1 |