Multi-step methods for random ODEs driven by Itô diffusions

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• 作者：Y. Asai^a ; ^b ; P.E. Kloeden^c ; ^{kloeden@math.uni-frankfurt.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34F05 ; 65C30 ; 60H25 ; 65L45 ; 65N40
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：294
• 期：Complete
• 页码：210-224
• 全文大小：787 K

文摘

Linear multi-step methods are derived for random ordinary differential equations (RODEs) driven by the solutions of Itô stochastic differential equations (SODEs) via strong Itô–Taylor schemes for SODEs. Due to the special structure of the RODE–SODE pair it is not necessary to restrict the intensity of the noise. Pathwise convergence is established as well as the B-stability of implicit multi-step methods. Numerical comparisons are provided for explicit schemes applied to a low dimensional RODE and implicit schemes applied to a high dimensional RODE obtained with the method of lines by spatially discretizing a random partial differential equation with finite difference quotients.