Y. Komori (2006), Weak high order stochastic Runge-Kutta methods, RIMS Kokyuroku 1505, 88-100.

Abstract
A new explicit stochastic Runge-Kutta (SRK) scheme of weak order 2 is proposed for non-commutative Stratonovich-type stochastic differential equations (SDEs), which is derivative-free, which attains order 4 for ordinary differential equations and which uses 2m-1 random variables for one step in the m-dimensional Wiener process case. It is compared with other derivative-free and weak second order schemes in a numerical experiment. In addition, the weak third order conditions are given as a preliminary to seeking higher weak order SRK schemes for multi-dimensional SDEs with one-dimensional Wiener process.

Note
Most of the material in this report has been superseded by Y. Komori (2007). Only the appendix is still current, in which weak third order conditions are shown for multi-dimensional SDEs with a scalar Wiener process.

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Last updated: 2009/11/24