ABSTRACT
We present an important family of Markov chains appearing naturally in many modelling frameworks, like epidemic theory or chemical reaction network dynamics. It is often impossible to get analytical results on the solutions of master equations associated with large and complicated gene network dynamics, and scientists rely most of the time on simulations. This is a good solution for getting ideas of what is going on in specific networks, but it is less useful to gather conceptual results. The linear noise approximation method provides a way of obtaining useful information through gaussian approximation: one can then consider the covariance matrix and try to understand noise sources, or to optimize network parameters to obtain required noise levels.
