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Keywords:
stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations
stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations
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.
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