Multi-step maruyama methods for stochastic delay differential equations

@inproceedings{Buckwar2007MultistepMM,
  title={Multi-step maruyama methods for stochastic delay differential equations},
  author={Evelyn Buckwar and Renate Winkler},
  year={2007}
}
Abstract In this article the numerical approximation of solutions of Ito 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.Β 

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