A natural extension of Markov processes and applications to singular SDEs
A talk in the Bielefeld Stochastic Summer series by Iulian Cimpean from Romanian Academy, Bucharest
We present a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made stuck in the added points, and it renders a new technique of constructing extended solutions to S(P)DEs from all starting points, in such a way that they are solutions at least after any strictly positive time. Concretely, we apply this extension to study SDEs with singular coefficients on an infinite dimensional state space, e.g. SPDEs of evolutionary type. This talk is based on joint work with L. Beznea and M. Röckner.
Within the CRC this talk is associated to the project(s): A5, B1, B2