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Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

2 Issues per year


CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.183
Source Normalized Impact per Paper (SNIP) 2017: 0.364

Mathematical Citation Quotient (MCQ) 2017: 0.27

Online
ISSN
1869-6082
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Volume 19, Issue 1

Issues

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

Abstract.

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

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Nick Lindemulder
Journal of Functional Analysis, 2017, Volume 272, Number 4, Page 1435
[2]
Roland Schnaubelt and Mark Veraar
Journal of Evolution Equations, 2017, Volume 17, Number 1, Page 523
[3]
Jan van Neerven, Mark Veraar, and Lutz Weis
Journal of Evolution Equations, 2015, Volume 15, Number 2, Page 361

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