The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 21, Number 3 (2011), 908-950.
Efficient simulation of nonlinear parabolic SPDEs with additive noise
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.
Ann. Appl. Probab., Volume 21, Number 3 (2011), 908-950.
First available in Project Euclid: 2 June 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 65C30: Stochastic differential and integral equations
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg. Efficient simulation of nonlinear parabolic SPDEs with additive noise. Ann. Appl. Probab. 21 (2011), no. 3, 908--950. doi:10.1214/10-AAP711. https://projecteuclid.org/euclid.aoap/1307020387