The Analytic solution for some non-linear stochastic differential equation by linearization (Linear-transform)

Abstract

In this paper, we study a reducible method which is called linearization(Linear-transform) for some non-linear stochastic differential equations (SDEs) to linear by using the Ito-integrated formula. And then finding their analytic solution, we compare the obtained solution for the nonlinear SDEs with the approximate solution by using numerical (Euler -Maruyama and Milstein) Methods.

Keywords

• stochastic differential equation
• ito formula
• reducible
• euler-maruyama & milstein