COMPARISON OF EULER MARUYAMA AND MILSTEIN METHOD FOR THE NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS.

Abstract

This paper presents an introduction to the concepts of numerical experiments involving stochastic differential equations (SDE) and the convergence of Euler-Maruyama method and Milstein method for the solution of stochastic differential equations (SDE). The Euler-Maruyama method is constructed within the ito integral framework. Milstein Method is derived from a truncation of the stochastic Taylor expansion of solution. The convergence of Euler-Maruyama and Milstein methods were compared.