Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1231.35324
Kunze, Markus; van Neerven, Jan
Approximating the coefficients in semilinear stochastic partial differential equations. (English)
[J] J. Evol. Equ. 11, No. 3, 577-604 (2011). ISSN 1424-3199; ISSN 1424-3202/e

Summary: We investigate, in the setting of UMD Banach spaces $E$, the continuous dependence on the data $A, F, G$ and $\xi $ of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form $$ \cases{\mathrm d}X(t) = [AX(t) + F(t, X(t))] \, {\mathrm d}t + G(t, X(t)) \, {\mathrm d}W_H(t),\quad t \in [0,T],\\ X(0) = \xi, \endcases$$ where $W _{H }$ is a cylindrical Brownian motion in a Hilbert space $H$. We prove continuous dependence of the compensated solutions $X(t) - e ^{tA } \xi $ in the norms $L ^{p }(\Omega ; \, C ^{\lambda }([0, T]; \, E))$ assuming that the approximating operators $A _{n }$ are uniformly sectorial and converge to $A$ in the strong resolvent sense and that the approximating nonlinearities $F _{n }$ and $G _{n }$ are uniformly Lipschitz continuous in suitable norms and converge to $F$ and $G$ pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite dimensional multiplicative noise.

MSC 2000:: *35R60 PDE with randomness
60H15 Stochastic partial differential equations
35K58
60J65 Brownian motion
46B09 Probabilistic methods in Banach space theory

Keywords: stochastic integration; Banach spaces; multiplicative noise

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]