MATHEMATICA BOHEMICA, Vol. 123, No. 1, pp. 7-32 (1998)

Maximal inequalities and space-time regularity
of stochastic convolutions

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:; Jan Seidler, Mathematical Institute, Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:

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

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