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Maximal inequalities and space-time regularity of stochastic convolutions. (English) Zbl 0903.60047
Summary: Space-time regularity of stochastic convolution integrals $$J=\int^._0 S(\cdot-r)Z(r)dW(r)$$ 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.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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