Regularity of the sample paths of a class of second order spde's

Details Regularity of the sample paths of a class of second order spde's Regularity of the sample paths of a class of second order spde's

2004-09-22

arxiv.org/abs/math/0409430v1

Mathematics

Probability

31 pages

Scientific paper

We study the sample path regularity of the solutions of a class of spde's which are second order in time and that includes the stochastic wave equation. Non-integer powers of the spatial Laplacian are allowed. The driving noise is white in time and spatially homogeneous. Continuing with the work initiated in Dalang and Mueller (2003), we prove that the solutions belong to a fractional $L^2$-Sobolev space. We also prove H\"older continuity in time and therefore, we obtain joint H\"older continuity in the time and space variables. Our conclusions rely on a precise analysis of the properties of the stochastic integral used in the rigourous formulation of the spde, as introduced by Dalang and Mueller. For spatial covariances given by Riesz kernels, we show that our results are optimal.

Affiliated with

Also associated with

No associations

Rating

Regularity of the sample paths of a class of second order spde's 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 Regularity of the sample paths of a class of second order spde's, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity of the sample paths of a class of second order spde's will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-442605