New regularity of kolmogorov equation and application on approximation of semi-linear spdes with Hölder continuous drifts

Abstract

In this paper, some new results on the the regularity of Kolmogorov equations associated to the infinite dimensional OU-process are obtained. As an application, the average $L^2$-error on $[0, T]$ of exponential integrator scheme for a range of semi-linear stochastic partial differential equations is derived, where the drift term is assumed to be Hölder continuous with respect to the Sobolev norm $\|·\|_{β}$ for some appropriate $β>0$. In addition, under a stronger condition on the drift, the strong convergence estimate is obtained, which covers the result of the SDEs with Hölder continuous drift.