Approximation Schemes for Stochastic Differential Equations in Hilbert Space

Abstract

For solutions of Itô–Volterra equations and semilinear evolution-type equations we consider approximations via the Milstein scheme, approximations by finite-dimensional processes, and approximations by solutions of stochastic differential equations (SDEs) with bounded coefficients. We prove mean-square convergence for finite-dimensional approximations and establish results on the rate of mean-square convergence for two remaining types of approximation.