Article
On the existence of weak variational solutions to stochastic differential equations
Communications on Stochastic Analysis (COSA)
Document Type
Article
Publication Date
3-1-2010
Abstract
We study the existence of weak variational solutions in a Gelfand triplet of real separable Hilbert spaces, under continuity, growth, and coercivity conditions on the coefficients of the stochastic differential equation. The laws of finite dimensional approximations are proved to weakly converge to the limit which is identified as a weak solution. The solution is an H– valued continuous process in L2 (Ω, C([0, T], H)) ∩ L2([0, T] × Ω, V ). Under the assumption of monotonicity the solution is strong and unique.
Disciplines
DOI
10.31390/cosa.4.1.02
Rights
© 2010 Louisiana State University
Citation Information
Leszek Gawarecki and Vidyadhar Mandrekar. "On the existence of weak variational solutions to stochastic differential equations" Communications on Stochastic Analysis (COSA) Vol. 4 Iss. 1 (2010) p. 1 - 20 ISSN: 0973-9599 Available at: http://works.bepress.com/leszek-gawarecki/7/