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

[摘要] 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. (C) 2016 Elsevier B.V. All rights reserved.

[发布日期] 2017-05-15

[效力级别]  Proceedings Paper

[关键词] Stratonovich SDEs;Stochastic Runge-Kutta methods;Quadratic invariants;Stochastic B-series;Order conditions