摘要
由于随机微分方程的全隐式Euler方法不是均方收敛的,一般认为它没有意义。然而,从运用计算机实现的角度来说几乎处处意义下的收敛和稳定比均方意义的收敛和稳定更具优势。针对线性随机微分方程,提出了一类全隐式Euler方法,证明了该方法生成的数值解几乎处处收敛,给出了该方法几乎处处稳定的充要条件。
The full implicit Euler methods for the stochastic differential equations were criticized for failing to converge to the true solutions in mean square. However, the almost sure convergence and stability were superior to the convergence and stability in mean square from the viewpoint of computer implementation. For the linear stochastic differential equations a class of the full implicit Euler methods was proposed, the numerical solution generated by it was almost surely convergent, and the necessary and sufficient condition of almost sure stability for the method were given.
出处
《系统仿真学报》
CAS
CSCD
北大核心
2009年第17期5403-5405,共3页
Journal of System Simulation
基金
福建省科技厅青年人才项目(2008F306010002)
关键词
线性随机微分方程
全隐式Euler方法
几乎处处收敛
几乎处处稳定
linear stochastic differential equations
full implicit Euler methods
almost sure convergence
almost sure stability
