an:01204015
Zbl 0903.60047
Peszat, Szymon; Seidler, Jan
Maximal inequalities and space-time regularity of stochastic convolutions
EN
Math. Bohem. 123, No. 1, 7-32 (1998).
00051393
1998
j
60H15
stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations
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 H??lder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.