Wednesday, December 11, 2019 - 14:00 in V3-201
On the local property of Markov processes
A talk in the Bielefeld Stochastic Afternoon series by
Iulian Cimpean from Romanian Academy, Bucharest
| Abstract: |
It is a well known principle that the continuity property of the paths of a cadlag Markov process corresponds to the "local" nature of the associated Kolmogorov operator. However, when starting from an operator defined on a class of test functions, or maybe from a semigroup of probability kernels on some general state space, it is a highly non-trivial task to rigorously construct such a "diffusion" Markov process. Since the seminal work of Feller and Ray, several powerful techniques have been developed, either for Feller semigroups or in the general framework of (possibly non-sectorial) Dirichlet forms. This talk is intended to offer yet another look at the subject; it is potential theoretical and it unifies previous results from different frameworks, into a general, energy-free, statement. Joint work with L. Beznea and M. Röckner.
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