Efficient simulation methods for stochastic differential equations

Abstract

The purpose of this study, was to improve the efficiency of simulations of stochastic differential equations. We first explain what such equations and their properties are. Then we derive some methods to simulate them. The first couple of these methods are generalizations of numerical integration methods, which are not new. After these methods we derive new methods with a different approach. To test these methods, we generate the stationary probability distribution of the process, and compare it to the theory. We do see improvements in terms of stability and accuracy in some cases, but further research into their efficiency is needed to be conclusive.