Approximating the coefficients in semilinear stochastic partial differential equations

摘要: We investigate, in the setting of UMD Banach spaces E, continuous dependence on data A, F, G and ξ mild solutions semilinear stochastic evolution equations with multiplicative noise form $$ \left\{ \begin{array}{l} {\rm d}X(t) = [AX(t) + F(t, X(t))] \, d}t G(t, X(t)) d}W_H(t),\quad t \in [0,T],\\ X(0) \xi, \end{array} \right. $$ where WH is a cylindrical Brownian motion Hilbert space H. prove compensated X(t) − etAξ norms Lp(Ω;Cλ([0, T]; E)) assuming that approximating operators An are uniformly sectorial converge to A strong resolvent sense nonlinearities Fn Gn Lipschitz suitable F pointwise. Our results applied class parabolic SPDEs finite dimensional noise.