A survey of Strong Convergent Schemes for the Simulation of Stochastic Differential Equations

Abstract

We considered strong convergent stochastic schemes for the simulation of stochastic differential equations. The stochastic Taylor's expansion, which is the main tool used for the derivation of strong convergent  schemes; the Euler Maruyama, Milstein scheme, stochastic multistep schemes, Implicit and Explicit schemes were considered. A simple SDE, which is known to have analytic solution, was used to illustrate the simulation technicalities. A MatLab script file was written to implement the Euler Maruyama and the Milstein schemes. The result showed graphically the closeness of the Milstein and the Euler Maruyama scheme as well as the error between the analytic result and the numerical approximation. The error appeared dispersed as t increases and tens to T.