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Multi-Step Maruyama Methods for Stochastic Delay Differential Equations |
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| Authors: | Evelyn Buckwar Renate Winkler |
| Institution: | 1. Institut für Mathematik , Humboldt-Universit?t zu Berlin , Berlin, Germany buckwar/winkler@mathematik.hu-berlin.de;3. Institut für Mathematik , Humboldt-Universit?t zu Berlin , Berlin, Germany |
| Abstract: | Abstract In this article the numerical approximation of solutions of Itô 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. |
| Keywords: | Linear multi-step Maruyama methods Stochastic delay differential equations Strong convergence Itô formula for stochastic delay differential equations |