Geodesic
Maximal inequalities and space-time regularity of stochastic convolutions
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 7-32.

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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.
DOI : 10.21136/MB.1998.126299
Classification : 60H15
Keywords: stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations 
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Peszat, Szymon; Seidler, Jan. Maximal inequalities and space-time regularity of stochastic convolutions. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 7-32. doi : 10.21136/MB.1998.126299. http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126299/

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