带有一个噪声的随机微分方程的全隐式格式（英文）  

Full implicit schemes for stochastic differential equations with one noise

作　　者：孙丽莹[1] 王丽瑾[1] 

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2016年第3期306-310,共5页Journal of University of Chinese Academy of Sciences

基　　金：Supported by National Natural Science Foundation of China(11471310,11071251)

摘　　要：通过将It型随机微分方程转换为等价的Stratonovich型和向后It型随机微分方程,构造出分别与Stratonovich型和向后It型随机微分方程相容的两种全隐式随机数值格式.这两种数值格式应用于带一个噪声的随机微分方程,且均为均方1阶收敛的.Two kinds of full implicit numerical schemes for stochastic differential equations in the Ito sense are given via construction of the numerical methods for the equivalent stochastic differential equations in the sense of Stratonovich and Backward-Ito. This approach could be applied to the stochastic differential equations with one noise, and we prove that the two methods which are generated by the equivalent stochastic differential equations are of mean-square order 1.

关 键 词：随机微分方程 全隐式数值格式 Ito型随机微分方程 Stratonovich型随机微分方程 

分 类 号：O241.8[理学—计算数学]