This article is cited in 8 papers

Approximation schemes for stochastic differential equations in Hilbert space

Yu. S. Mishura, G. M. Shevchenko

National Taras Shevchenko University of Kyiv

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.

Keywords: stochastic differential equations in Hilbert space, discrete-time approximations, Milstein scheme, Itô–Volterra type equation.

Received: 29.09.2003
Revised: 14.04.2006

DOI: 10.4213/tvp35

 English version: Theory of Probability and its Applications, 2007, 51:3, 442–458

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