Digital simulation of white noise differential equations using Runge Kutta method

In this paper we study some numerical integration methods based on the classical Runge Kutta formula for the digital simulation of differential equations driven by white noise. As a result, we show that the n-th moments of the Riggs and Phillips approximations (1987) converge to those of the solution of Ito equation, which is in contrast to the case of the standard Runge Kutta method. Therefore we must convert the white noise differential equations into the equivalent Ito equations before we use the Riggs and Phillips method for digital simulation. An improved version of the Riggs and Phillips method is also presented.