Magnus methods for stochastic delay-differential equations.

Stochastic delay-differential equations (SDDEs) are SDEs with dependence on past times. Applications of SDDEs are found in financial modelling, engineering, and various sciences. At present, existing numerical methods that are used for SDDEs are stochastic Taylor approximations. We propose Magnus-type modifications to these schemes in the case of finitely many delays, for improved accuracy with no additional computation cost. These modified schemes are applied step-by-step between delay times. We present error graphs, showing improvements for strong-order 1/2 and 1 schemes, when combined with Magnus methods. We also provide discussion about further applications to equations more general than those considered in these pages. [ABSTRACT FROM AUTHOR]