  Few analytical methods exist for quantitative studies of large fluctuations
in stochastic systems. In this article, we develop a simple diagrammatic
approach to the Chemical Master Equation that allows us to calculate multi-time
correlation functions which are accurate to a any desired order in van Kampen's
system size expansion. Specifically, we present a set of Feynman rules from
which this diagrammatic perturbation expansion can be constructed
algorithmically. We then apply the methodology to derive in closed form the
leading order corrections to the linear noise approximation of the intrinsic
noise power spectrum for general biochemical reaction networks. Finally, we
illustrate our results by describing noise-induced oscillations in the
Brusselator reaction scheme which are not captured by the common linear noise
approximation.
