Generalized two-step Milstein methods for stochastic differential equations

摘要

ABSTRACT The main aim of this study is to propose a class of generalized two-step Milstein methods for solving Itô stochastic differential equations. We study their mean-square consistency and mean-square convergence and derive some conditions for the linear mean-square stability of the generalized two-step Milstein methods. Numerical examples are given to confirm the theoretical results.