Solving parabolic stochastic partial differential equations via averaging over characteristics
Solving parabolic stochastic partial differential equations via averaging over characteristics
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DOI：
10.1090/s0025-5718-09-02250-9
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发表时间：
2009-03
期刊：
影响因子：
--
通讯作者：
G. Milstein;M. Tretyakov
中科院分区：
文献类型：
--
作者：
G. Milstein;M. Tretyakov
将特征线法（特征线平均法）和弱意义的随机微分方程数值积分方法与Monte Carlo技术相结合，提出了求解线性随机偏微分方程的数值方法。得到了它们的均方收敛阶和几乎处处收敛阶。被认为是一个方差减少技术的蒙特卡罗程序。构造了线性和半线性随机偏微分方程的分层方法，并证明了相应的收敛性定理。开发的方法是支持数值实验。
The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure convergence are obtained. A variance reduction technique for the Monte Carlo procedures is considered. Layer methods for linear and semilinear SPDEs are constructed and the corresponding convergence theorems are proved. The approach developed is supported by numerical experiments.