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Journal of Applied Analysis

Editor-in-Chief: Fechner, Włodzimierz / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

CiteScore 2018: 0.45

SCImago Journal Rank (SJR) 2018: 0.181
Source Normalized Impact per Paper (SNIP) 2018: 0.845

Mathematical Citation Quotient (MCQ) 2018: 0.20

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Volume 19, Issue 1


Maximal regularity for stochastic integral equations

Gertrud Desch
  • Department of Mathematics and Scientific Computing, Karl-Franzens-University Graz, Heinrichstrasse 36, 8010 Graz, Austria
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/ Stig-Olof Londen
Published Online: 2013-06-04 | DOI: https://doi.org/10.1515/jaa-2013-0006


We examine the stochastic parabolic integral equation of convolution type

where takes values in with a σ-finite measure space, and . The linear operator A maps into , is nonnegative and admits a bounded H-calculus on . The kernels are powers of t, with , , and , . We show that, in the maximal regularity case, where , one has the estimate

where c is independent of G. Here and denotes fractional integration if , and fractional differentiation if , both with respect to the t-variable. The proof relies on recent work on stochastic differential equations by van Neerven, Veraar and Weis, and extends their maximal regularity result to the integral equation case.

Keywords: Stochastic integral equations; maximal regularity; H∞-calculus

About the article

Received: 2011-03-02

Revised: 2012-04-10

Accepted: 2012-06-25

Published Online: 2013-06-04

Published in Print: 2013-06-01

Citation Information: Journal of Applied Analysis, Volume 19, Issue 1, Pages 125–140, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/jaa-2013-0006.

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Citing Articles

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Nick Lindemulder
Journal of Functional Analysis, 2017, Volume 272, Number 4, Page 1435
Roland Schnaubelt and Mark Veraar
Journal of Evolution Equations, 2017, Volume 17, Number 1, Page 523
Jan van Neerven, Mark Veraar, and Lutz Weis
Journal of Evolution Equations, 2015, Volume 15, Number 2, Page 361

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