HIGHER-ORDER RUNGE-KUTTA METHOD FOR ITÔ STOCHASTIC DIFFERENTIAL EQUATIONS WITH A NON-DEGENERATE DIFFUSION MATRIX
In this paper, a new pathwise approximation method is constructed to obtain approximate solutions of order for Itô stochastic differential equations (SDEs). The new method does not require the simulation of the iterated stochastic integrals they are replaced by random variables with the same moments conditional on the linear term. The construction of the scheme is based on stochastic Itô-Taylor expansion and employing the Runge-Kutta method. It has been assumed a non-degenerated and global Lipschitz condition for the diffusion matrix Numerical example is provided to support the validity of this new method.
stochastic differential equations, pathwise approximation, Runge-Kutta method, Itô-Taylor expansion.