Exact computation of current cumulants in small Markovian systems

We describe an algorithm computing the exact value of the mean current, its variance, and higher order cumulants for stochastic driven systems. The method uses a Rayleigh-Schrödinger perturbation expansion of the generating function of the current, and can be extended to compute covariances of multiple currents. As an example of application of the method, we give numerical evidence for a simple relation [Eq. (5)] between the second and the fourth cumulants of the current in a symmetric exclusion process.