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

Abstract

The purpose of this paper is to correct errors presented recently in the paper [Lv et al. J Stat Phys 149:619-628 (2012)], where the authors analyzed Fractional Fokker-Planck equation (FFPE) with space-time dependent drift F(x, t) = F(x) f(t) and diffusion D(x, t) = D(x)d̃(t) coefficients in the factorized form. We show an important drawback in the derivation of the stochastic representation of FFPE presented in the aforementioned paper, which makes the whole proof wrong. Moreover, we present a correct proof of their result in even more general case, when both drift and diffusion can have any, not necessarily factorized, form. © 2014 The Author(s).