Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions

被引：11
作者：
Lang, Annika [1 ,2 ]
Petersson, Andreas [1 ,2 ]
Thalhammer, Andreas [3 ]
机构：
[1] Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden
[2] Univ Gothenburg, S-41296 Gothenburg, Sweden
[3] Johannes Kepler Univ Linz, Inst Stochast, Doktoratskolleg Computat Math, A-4040 Linz, Austria
来源：
BIT NUMERICAL MATHEMATICS | 2017年 / 57卷 / 04期
基金：
奥地利科学基金会; 瑞典研究理事会;
关键词：
Asymptotic mean-square stability; Numerical approximations of stochastic differential equations; Linear stochastic partial differential equations; Levy processes; Rational approximations; Galerkin methods; Spectral methods; Finite element methods; Euler-Maruyama scheme; Milstein scheme; MONTE-CARLO METHOD; SIMULATION; DRIVEN;
D O I：
10.1007/s10543-017-0684-7
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential equations and necessary and sufficient conditions ensuring mean-square stability are given. They are applied to typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler methods. Furthermore, results on the relation to stability properties of corresponding analytical solutions are provided. Simulations of the stochastic heat equation illustrate the theory.
引用
收藏
页码：963 / 990
页数：28
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