Fractional Fokker-Planck Equation with Space and Time Dependent Drift and Diffusion

Abstract

In this paper, we aim to answer the question proposed by Magdziarz (Stoch. Proc. Appl. 119:3238–3252, 2009), i.e. we investigate the solution of an anomalous diffusion equation with time and space dependent force and diffusion coefficient. First, we try to find the stochastic representation of this equation, which means the PDF of this stochastic process is rightly the solution of the equation we aim to solve. Then, we also simulate the sample paths of the stochastic process. At last, taking advantage of the stochastic representation method, we employed Monte Carlo method to approximate the solution of the mentioned equation.