Order conditions for stochastic Runge-Kutta methods preserving quadratic invariants of Stratonovich SDEs

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• 作者：Sverre Anmarkrud^a ; ^{sverre.anmarkrud@nmbu.no} ; Anne Kvæ ; rnø ; ^b ; ^{anne@math.ntnu.no}
• 关键词：Stratonovich SDEs ; Stochastic Runge&ndash ; Kutta methods ; Quadratic invariants ; Stochastic B-series ; Order conditions
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：316
• 期：Complete
• 页码：40-46
• 全文大小：688 K
• 卷排序：316

文摘

In this paper we prove that for a stochastic Runge–Kutta method, the conditions for preserving quadratic invariants work as simplifying assumptions. For such methods, the method coefficients only have to satisfy one condition for each unrooted tree. This is a generalization of the result obtained for deterministic Runge–Kutta methods by Sanz-Serna and Abia in 1991.