Abstract.
Existence of solutions to martingale problems corresponding to singular dissipative stochastic equations in Hilbert spaces are proved for any initial condition. The solutions for the single starting points form a conservative diffusion process whose transition semigroup is shown to be strong Feller. Uniqueness in a generalized sense is proved also, and a number of applications is presented.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 November 2001 / Revised version: 8 April 2002 / Published online: 10 September 2002
An erratum to this article is available at http://dx.doi.org/10.1007/s00440-008-0179-1.
Rights and permissions
About this article
Cite this article
Da Prato, G., Röckner, M. Singular dissipative stochastic equations in Hilbert spaces. Probab Theory Relat Fields 124, 261–303 (2002). https://doi.org/10.1007/s004400200214
Issue Date:
DOI: https://doi.org/10.1007/s004400200214