Efficient simulation of nonlinear parabolic SPDEs with additive noise
Abstract
Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been introduced. The key idea was to use suitable linear functionals of the noise process in the numerical scheme which allow a higher approximation order to be obtained. Following this approach, a new simplified version of the scheme in the above named reference is proposed and analyzed in this article. The main advantage of the convergence result given here is the higher convergence order for nonlinear parabolic SPDEs with additive noise, although the used numerical scheme is very simple to simulate and implement.
Keywords
Cite
@article{arxiv.1210.8320,
title = {Efficient simulation of nonlinear parabolic SPDEs with additive noise},
author = {Arnulf Jentzen and Peter Kloeden and Georg Winkel},
journal= {arXiv preprint arXiv:1210.8320},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP711 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)