Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus

Xiaojie  Wang

doi:10.3934/dcds.2016.36.481

Article Contents

2016, Volume 36, Issue 1: 481-497. Doi: 10.3934/dcds.2016.36.481

This issue Previous Article Center specification property and entropy for partially hyperbolic diffeomorphisms Next Article Radial sign-changing solution for fractional Schrödinger equation

Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus

Xiaojie Wang^1,

1.
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan

Received: August 2014

Revised: March 2015

Published: May 2017

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Abstract

This paper deals with the weak error estimates of the exponential Euler method for semi-linear stochastic partial differential equations (SPDEs). A weak error representation formula is first derived for the exponential integrator scheme in the context of truncated SPDEs. The obtained formula that enjoys the absence of the irregular term involved with the unbounded operator is then applied to a parabolic SPDE. Under certain mild assumptions on the nonlinearity, we treat a full discretization based on the spectral Galerkin spatial approximation and provide an easy weak error analysis, which does not rely on Malliavin calculus.

Keywords:

Semi-linear stochastic partial differential equations,
additive noise,
exponential Euler scheme,
weak convergence.

Mathematics Subject Classification: Primary: 60H35, 60H15; Secondary: 65C30.

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