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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

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

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