论文信息 - Order Conditions of Stochastic Runge-Kutta Methods by B-Series

Order Conditions of Stochastic Runge-Kutta Methods by B-Series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

Kevin Burrage | Pamela M. Burrage | K. Burrage | P. Burrage

[1] W. Rüemelin. Numerical Treatment of Stochastic Differential Equations , 1982 .

[2] Yoshio Komori,et al. Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations , 1997 .

[3] Kevin Burrage,et al. High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula , 1999 .

[4] J. Butcher. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[5] Kevin Burrage,et al. General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems , 1998 .

[6] S. Zacks,et al. Introduction to stochastic differential equations , 1988 .

[7] Kevin Burrage,et al. A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations , 1997 .

[8] G. Milstein. Numerical Integration of Stochastic Differential Equations , 1994 .

[9] K. Burrage,et al. High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations , 1996 .

[10] G. Maruyama. Continuous Markov processes and stochastic equations , 1955 .

[11] P. Kloeden,et al. Numerical Solution of Stochastic Differential Equations , 1992 .

[12] Pamela Burrage,et al. Runge-Kutta methods for stochastic differential equations , 1999 .