Title
On the existence of weak variational solutions to stochastic differential equations
Document Type
Article
Publication Date
3-1-2010
Publication Title
Communications on Stochastic Analysis (COSA)
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.
Volume
4
Issue
1
First Page
1
Last Page
20
DOI
10.31390/cosa.4.1.02
ISSN
0973-9599
Rights
© 2010 Louisiana State University
Recommended Citation
Gawarecki, Leszek and Mandrekar, Vidyadhar, "On the existence of weak variational solutions to stochastic differential equations" (2010). Mathematics Publications. 1.
https://digitalcommons.kettering.edu/mathematics_facultypubs/1
