Studying Some Stochastic Differential Equations with trigonometric terms with Application

Abstract

In this paper we look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.