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MATHEMATICA BOHEMICA, Vol. 123, No. 1, pp. 7-32 (1998)
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#
Maximal inequalities and space-time regularity

of stochastic convolutions

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Szymon Peszat, Jan Seidler

* Szymon Peszat*, Institute of Mathematics, Polish Academy of Sciences, Sw. Tomasza 30/7, 31-027 Krakow; and Institute of Mathematics, University of Mining and Metallurgy, Mickiewicza 30, 30-059 Krakow, Poland, e-mail: ` peszat@uci.agh.edu.pl`; * Jan Seidler,* Mathematical Institute, Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: ` seidler@math.cas.cz`

**Abstract:** 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 Hölder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.

**Keywords:** stochastic convolutions, maximal inequalities, regularity of stochastic partial differential equations

**Classification (MSC2000):** 60H15

**Full text of the article:**

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