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

Direct numerical method for counting statistics in stochastic processes