Maximal inequalities and space-time regularity of stochastic convolutions. (English) Zbl 0903.60047

Peszat, Szymon; Seidler, Jan

Math. Bohem. 123, No. 1, 7-32 (1998).

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)

Keywords:

stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations