Abstract
The approximated normal random variable which has similar moment properties to the normal random variable is used in the weak approximation of stochastic differential equations. In this paper we describe three types of the approximated normal random variable, namely multi-point distribution, rectangular approximation and polygonal line approximation. And asymptotic stability of the Euler-Maruyama simplified scheme for the approximated normal random variable is studied. We also present some numerical results which demonstrate the stability properties.
