10.1016/j.crma.2007.12.005
Beznea, Lucian
Lucian
Beznea
Boboc, Nicu
Nicu
Boboc
Röckner, Michael
Michael
Röckner
Markov processes associated with L-P-resolvents, applications to quasi-regular Dirichlet forms and stochastic differential equations
Elsevier
2008
2010-04-28T11:50:21Z
2019-07-08T13:07:23Z
journal_article
https://pub.uni-bielefeld.de/record/1592122
https://pub.uni-bielefeld.de/record/1592122.json
1631-073X
We show that every C-0-resolvent on L-p(E, mu), where (E, beta) is a Lusin measurable space and mu is a or-finite measure on beta, has an associate sufficiently regular Markov process on a (larger) Lusin topological space containing E as a Borel subset. We give general conditions on the resolvent's generator such that the above process lives on E. We present two applications: (i) we settle a question of G. Mokobodzki on the existence of a (Lusin) topology on E having beta as Borel sigma-algebra such that a given Dirichlet form on L-2(E, mu) becomes quasi-regular; (ii) we solve stochastic differential equations on Hilbert spaces in the sense of a martingale problem.