We discuss existence, uniqueness, and space-time HÃ¶lder regularity for solutions of the parabolic stochastic evolution equation (dU (t) = (AU (t) + F (t, U (t))) dt + B(t, U (t)) dW H (t), t âˆˆ [0, Tâ€¦ (More)

In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise isâ€¦ (More)

We prove maximal Lp-regularity for the stochastic evolution equation( dU(t) + AU(t) dt = F (t, U(t)) dt + B(t, U(t)) dWH(t), t âˆˆ [0, T ], U(0) = u0, under the assumption that A is a sectorialâ€¦ (More)

We investigate the transition semigroup of the solution to a sto-chastic evolution equation dX(t) = AX(t) dt + dW H (t), t â‰¥ 0, where A is the generator of a C 0-semigroup S on a separable realâ€¦ (More)

In this paper we construct a theory of stochastic integration of processes with values in L(H,E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingaleâ€¦ (More)

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an ItÃ´ formula is proved which is applied to prove the existence ofâ€¦ (More)

We study the asymptotic behaviour of individual orbits T (Â·)x of a uniformly bounded C0-semigroup {T (t)}tâ‰¥0 with generator A in terms of the singularities of the local resolvent (Î»âˆ’ A)âˆ’1x on theâ€¦ (More)

Let f : R+ â†’ X be a bounded, strongly measurable function with values in a Banach space X, and let iE be the singular set of the Laplace transform fÌƒ in iR. Suppose that E is countable and Î± âˆ¥âˆ¥âˆ«âˆž 0 eâ€¦ (More)

Noting that every L-space satisfies a randomized version of the UMD property, we show how a general stochastic Fubini theorem for the stochastic integral of operatorvalued processes with respect toâ€¦ (More)