System size expansion for the probability distribution of the Master equation

Philipp Thomas, Ramon Grima

Published 2014-11-13Version 1

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive a closed-form approximation of the probability distribution of the Master Equation using van Kampen's system size expansion. The solution is given in two alternative formulations: a series with continuous and a series with discrete support that can be systematically truncated. We show that the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions.