Existence of weak solutions to stochastic evolution inclusions

Details Existence of weak solutions to stochastic evolution inclusions Existence of weak solutions to stochastic evolution inclusions

2004-07-29

arxiv.org/abs/math/0407512v2

Mathematics

Probability

Scientific paper

We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is more heneral than the Lipschitz condition. We prove the existence of a mild solution to this problem. This solution is not "strong" in the probabilistic sense, that is, it is not defined on the underlying probability space, but on a larger one, which provides a "very good extension" in the sense of Jacod and Memin. Actually, we construct this solution as a Young measure, limit of approximated solutions provided by the Euler scheme. The compactness in the space of Young measures of this sequence of approximated solutions is obtained by proving that some measure of noncompactness equals zero.

Affiliated with

Also associated with

No associations

Rating

Existence of weak solutions to stochastic evolution inclusions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence of weak solutions to stochastic evolution inclusions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence of weak solutions to stochastic evolution inclusions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457537