2012 ³12 Á

Abstract A new explicit split-step Milstein method for solving linear Itô stochastic differential equations (SDEs) with a constant time delay is introduced. The Itô-Taylor expansion is employed to prove the strong convergence, which inproves the convergence results of known split-step methods for stochastic delay differential equations (SDDEs). Numerical experiments confirm the theoretical results. Key words stochastic delay differential equation; Milstein scheme; split-step; strong convergence