Direct numerical method for counting statistics in stochastic processes

Details Direct numerical method for counting statistics in stochastic processes Direct numerical method for counting statistics in stochastic processes

2010-02-23

arxiv.org/abs/1002.4247v1

J. Stat. Mech. P06013 (2010)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 figures

Scientific paper

We propose a direct numerical method to calculate the statistics of the number of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary moments of the probability distribution of the number of transitions are in principle calculated by solving numerically a system of coupled differential equations. As an example, a two state model with a time-dependent transition matrix is considered and the first, second and third moments of the current are calculated. This calculation scheme is applicable for any stochastic process with a finite state space, and it would be helpful to study current statistics in nonequilibrium systems.

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