Volume 36 • Number 3 • 2013   • A Systematic Derivation of Stochastic Taylor Methods for Stochastic Delay Differential Equations Norhayati Rosli, Arifah Bahar, S. H. Yeak and X. Mao Abstract. This article demonstrates a systematic derivation of stochastic Taylor methods for solving stochastic delay differential equations (SDDEs) with a constant time lag, $r>0$. The derivation of stochastic Taylor expansion for SDDEs is presented. We provide the convergence proof of one--step methods when the drift and diffusion functions are Taylor expansion. It is shown that the approximation solutions for SDDEs converge in the $L^2$-norm. 2010 Mathematics Subject Classification: 65C99 Full text: PDF