Y. Komori (2007), Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations, Journal of Computational and Applied Mathematics, 206 (1), 158-173.

Abstract
A new explicit stochastic Runge-Kutta scheme of weak order 2 is proposed for non-commutative stochastic differential equations (SDEs), which is derivative-free and which attains order 4 for ordinary differential equations. The scheme is directly applicable to Stratonovich SDEs and 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 numerical experiments.

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