SDE BASED REGRESSION FOR LINEAR RANDOM PDEs

被引:5
作者
Anker, Felix [1 ]
Bayer, Christian [1 ]
Eigel, Martin [1 ]
Ladkau, Marcel [1 ]
Neumann, Johannes [1 ]
Schoenmakers, John [1 ]
机构
[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany
关键词
partial differential equations with random coefficients; random PDE; uncertainty quantification; Feynman-Kac; stochastic differential equations; stochastic simulation; stochastic regression; Monte Carlo; Euler Maruyama; PARTIAL-DIFFERENTIAL-EQUATIONS; STOCHASTIC COLLOCATION METHOD; RANDOM INPUT DATA; RANDOM-COEFFICIENTS; ELLIPTIC PROBLEMS; APPROXIMATIONS; OPTIONS;
D O I
10.1137/16M1060637
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A simulation based method for the numerical solution of PDEs with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation (SDE) driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behavior.
引用
收藏
页码:A1168 / A1200
页数:33
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