  The past decade has seen a revived interest in the unavoidable or intrinsic
noise in biochemical and genetic networks arising from the finite copy number
of the participating species. That is, rather than modeling regulatory networks
in terms of the deterministic dynamics of concentrations, we model the dynamics
of the probability of a given copy number of the reactants in single cells.
Most of the modeling activity of the last decade has centered on stochastic
simulation of individual realizations, i.e., Monte-Carlo methods for generating
stochastic time series. Here we review the mathematical description in terms of
probability distributions, introducing the relevant derivations and
illustrating several cases for which analytic progress can be made either
instead of or before turning to numerical computation.
