Stochastic maximal $L^p$-regularity

Details Stochastic maximal $L^p$-regularity Stochastic maximal $L^p$-regularity

2010-04-08

arxiv.org/abs/1004.1309v4

Annals of Probability 2012, Vol. 40, No. 2, 788-812

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP626 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP626

In this article we prove a maximal $L^p$-regularity result for stochastic convolutions, which extends Krylov's basic mixed $L^p(L^q)$-inequality for the Laplace operator on ${\mathbb{R}}^d$ to large classes of elliptic operators, both on ${\mathbb{R}}^d$ and on bounded domains in ${\mathbb{R}}^d$ with various boundary conditions. Our method of proof is based on McIntosh's $H^{\infty}$-functional calculus, $R$-boundedness techniques and sharp $L^p(L^q)$-square function estimates for stochastic integrals in $L^q$-spaces. Under an additional invertibility assumption on $A$, a maximal space--time $L^p$-regularity result is obtained as well.

Affiliated with

Also associated with

No associations

Rating

Stochastic maximal $L^p$-regularity 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 Stochastic maximal $L^p$-regularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic maximal $L^p$-regularity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-713293