Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises

被引：27

作者：

Barth, Andrea ^{[1
]}

Lang, Annika ^{[1
]}

机构：

[1] ETH, Seminar Angew Math, CH-8092 Zurich, Switzerland

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2012年 / 66卷 / 03期

基金：

欧洲研究理事会;

关键词：

Finite element method; Stochastic partial differential equation; Martingale; Galerkin method; Zakai equation; Advection-diffusion PDE; Milstein scheme; Karhunen-Loeve expansion; Nonequidistant time stepping; PARTIAL-DIFFERENTIAL-EQUATIONS; ZAKAI TYPE DRIVEN; NUMERICAL APPROXIMATION; SURE CONVERGENCE; SIMULATION; SPDES; SCHEME;

D O I：

10.1007/s00245-012-9176-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, cA dlA g, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L (2) and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.

引用

页码：387 / 413

页数：27

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