Asymmetric random walks and drift-diffusion
Department of Mathematical Sciences, Rensselaer Polytechnic Institute - Troy, NY 12180-3590, USA
Received: 30 November 2012
Accepted: 19 April 2013
To obtain the drift-diffusion equation from an asymmetric random walk it has been required that the left and right jump probabilities are approximately equal. It is shown here that such a restriction is not needed. Using multiple scales the equation is derived, where the scales are based on the advection and diffusion scales.
PACS: 05.40.Fb – Random walks and Levy flights / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 02.30.Mv – Approximations and expansions
© EPLA, 2013