A perturbation result for semi-linear stochastic differential equations in UMD Banach spaces

作者：Cox Sonja Gisela^*; Hausenblas Erika

来源：Journal of Evolution Equations, 2013, 13(4): 795-827.

DOI：10.1007/s00028-013-0203-5

• Perturbations
• Stochastic differential equations
• Stochastic convolutions
• Stochastic partial differential equations
• Yosida approximation

We consider the effect of perturbations of A on the solution to the following semi-linear parabolic stochastic partial differential equation: {dU(t) = AU(t) dt + F (t, U(t)) dt + G(t, U(t)) dW(H)(t), T %26gt; 0; U(0) = x(0). Here, A is the generator of an analytic C (0)-semigroup on a UMD Banach space X, H is a Hilbert space, W (H) is an H-cylindrical Brownian motion, , and for some , where denotes the type of the Banach space and denotes the fractional domain space or extrapolation space corresponding to A. We assume F and G to satisfy certain global Lipschitz and linear growth conditions. %26lt;br%26gt;Let A (0) denote the perturbed operator and U (0) the solution to (SDE) with A substituted by A (0). We provide estimates for in terms of . Here, is assumed to satisfy . The work is inspired by the desire to prove convergence of space approximations of (SDE). In this article, we prove convergence rates for the case that A is approximated by its Yosida approximation.

• 出版日期2013-12