Stochastic maximal Lp-regularity

By J. V. Neerven, Mark Veraar, Lutz Weis. 2010

94 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e89db45c014e0aaf57751dc7b411a3dc99375ba8

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Citations in the corpus

Maximal $L^p$-regularity for stochastic evolution equations (2011, background): “ARK VERAAR, AND LUTZ WEIS abstract operator-theoretic properties of the operators governing the equation, has yet to be developed. A ﬁrst step towards such a theory has been taken in our recent paper [68], where it was shown that if Ais a sectorial operator with a bounded H∞-calculus of angle <1 ”
Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise (2011, methodology): “There exist some generalizations of this result, for instance, to Banach space valued integrands [5], to the case p > 2 [18], and to Lévy noise [2].”
Traces and embeddings of anisotropic function spaces (2012, unknown): “Stochastic parabolic equations and Volterra integral equations (see [30, 46, 47]) are further scenarios in which intersection spaces, even in an abstract form, come naturally into play.”