Balanced Milstein Methods for Ordinary SDEs

Abstract

Convergence, consistency, stability and pathwise positivity of balanced Milstein methods for numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This family of numerical methods represents a class of highly efficient linear-implicit schemes which generate mean square converging numerical approximations with qualitative improvements and global rate 1. 0 of mean square convergence, compared to commonly known numerical methods for SDEs with Lipschitzian coefficients.