Biased random walks, partial differential equations and update schemes

Abstract

There is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a Fokker-Planck equation is used to describe the evolution of a collection of noninteracting asymmetric random walkers. The resulting continuum description is highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to the macroscopic description of stochastic local movement rules in agent-based models. doi:10.1017/S1446181113000369