Topic: A natural extension of Markov processes and applications to singular SDEs
Speaker: Professor Michael Röckner
Event date: 11/4/2019
Event time: 16:00 pm
Venue: Lecture Hall 1506, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: We develop a general method for extending Markov processes to a larger state space such that the added points form apolar set. The so obtained extension is an improvement on the standardtrivial 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 afterany strictly positive time. Concretely, we adopt this strategy to study SDEs with singular coefficients on an infinite dimensional state space (e.g. SPDEsof evolutionary type), for which one often encounters the situation where notevery point in the space is allowed as an initial condition. The same can happen when constructing solutions of martingale problems or Markov processes from (generalized) Dirichlet forms, to which our new technique also applies. Joint work with: Lucian Beznea (Romanian Academy, Bucharest, Romania)，Iulian Cîmpean (Romanian Academy, Bucharest, Romania).