关键词: 随机微分方程, 全隐式数值格式, Itô, 型随机微分方程, Stratonovich型随机微分方程

Abstract:

Two kinds of full implicit numerical schemes for stochastic differential equations in the Itô sense are given via construction of the numerical methods for the equivalent stochastic differential equations in the sense of Stratonovich and Backward-Itô. 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.

Key words: stochastic differential equations, full implicit numerical schemes, stochastic differential equations in the Itô, sense, stochastic differential equations in the Stratonovich sense