Split-step backward balanced Milstein methods for stiff stochastic systems

Abstract

In this paper we discuss split-step backward balanced Milstein methods for solving Itô stochastic differential equations (SDEs). Four families of methods, a family of drifting split-step backward balanced Milstein (DSSBBM) methods, a family of modified split-step backward balanced Milstein (MSSBBM) methods, a family of drifting split-step backward double balanced Milstein (DSSBDBM) methods and a family of modified split-step backward double balanced Milstein (MSSBDBM) methods, are constructed in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.