stochastic linear multi-step Maruyama method stochastic delay differential euqations $L_p$-convergence Multi-step Maruyama methods for stochastic delay differential equations Evelyn Buckwar Buckwar Evelyn Renate Winkler Winkler Renate Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2004-15

Multi-step Maruyama methods for stochastic delay differential equations

Evelyn Buckwar , Renate Winkler

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2004-15

MSC 2000

60H35 Computational methods for stochastic equations
65C30 Stochastic differential and integral equations

Abstract
In this paper the numerical approximation of solutions of It{\^o} stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their $L_p$-consistency, numerical $L_p$-stability and $L_p$-convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.

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