On the Roles of Brownian Motion in the Determination Of Numerical Solution of Stochastic Differential Equations

Authors: 1Ganiyu A.A., 2Olademo J.O. Ani, and 3Akinmuyise M.F.                             

1,2,3Department of Mathematics, Adeyemi College of Education, Ondo

This paper examines the nature of Brownian motion, stochastic differential equations (SDEs) and the roles played by Brownian motion in the determination of numerical solution of SDEs. To observe the roles of Brownian motion in the solution of SDEs, two stochastic differential equation problems have been provided. Solutions to the two problems are provided using two numerical methods. The numerical solutions of the two methods are then compared with the exact solution of the given problems. To observe the behaviour of the solution, simulation curves are also constructed.