Article

 Title: Maximal inequalities and space-time regularity of stochastic convolutions (English) Author: Peszat, Szymon Author: Seidler, Jan Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 123 Issue: 1 Year: 1998 Pages: 7-32 Summary lang: English . Category: math . Summary: Space-time regularity of stochastic convolution integrals J = {\int^\cdot_0 S(\cdot-r)Z(r)W(r)} driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated. The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator. Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well. (English) Keyword: stochastic convolutions Keyword: maximal inequalities Keyword: regularity of stochastic partial differential equations MSC: 60H15 idZBL: Zbl 0903.60047 idMR: MR1618707 DOI: 10.21136/MB.1998.126299 . Date available: 2009-09-24T21:28:51Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/126299 . Reference: [1] P.-L. Chow J.-L. Jiang: Stochastic partial differential equations in Hölder spaces.Probab. Theory Related Fields 99 (1994), 1-27. MR 1273740, 10.1007/BF01199588 Reference: [2] G. Da Prato S. Kwapień J. Zabczyk: Regularity of solutions of linear stochastic equations in Hilbert spaces.Stochastics 23 (1987), 1-23. MR 0920798 Reference: [3] G. Da Prato J. Zabczyk: A note on semilinear stochastic equations.Differential Integral Equations 1 (1988), 143-155. MR 0922558 Reference: [4] G. Da Prato J. 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