Stabilities of non-standard Euler-Maruyama scheme’s for Vasicek and geometric brownian motion models

Abstract

Stochastic differential equations (SDEs) are a powerful tool for modeling certain random trajectories of diffusion phenomena in the physical, ecological, economic, and management sciences. However, except in some cases, it is generally impossible to find an explicit solution to these equations. In this case, the numerical approach is the only favorable possibility to find an approximative solution. In this paper, we present the mean and mean-square stability of the Non-standard Euler-Maruyama numerical scheme using the Vasicek and geometric Brownian motion models.