Szymon Peszat, Institute of Mathematics, Polish Academy of Sciences, Sw. Tomasza 30/7, 31-027 Krakow; and Institute of Mathematics, University of Mining and Metallurgy, Mickiewicza 30, 30-059 Krakow, Poland, e-mail: peszat@uci.agh.edu.pl; Jan Seidler, Mathematical Institute, Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: seidler@math.cas.cz
Abstract: 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.
Keywords: stochastic convolutions, maximal inequalities, regularity of stochastic partial differential equations
Classification (MSC 1991): 60H15
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
