Stochastic Differential Equations on Fractal Sets

Abstract

In this manuscript, we review fractal calculus and random processes. Random variables and processes on totally disconnected fractal sets are defined. Random walks on fractal middle-xi Cantor sets are suggested and corresponding variances are given which are power laws. The mean square stochastic calculus is generalized on fractal sets, which can lead to the standard case by setting dimension . Furthermore, we solve a fractal stochastic differential equation using the Frobenius method. Graphs are presented to give more details.