Stochastic reaction networks are widespread in physical, chemical
and biological systems. These networks are commonly simulated
by Monte Carlo methods such as the Gillespie algorithm.
In this talk I will present two novel equation-based methods
for the analysis of stochastic networks. The multiplane method is a
dimensional-reduction method based on the master equation.
The moment equations method consists of a closed set of equations for the
first and second moments of the distribution of population sizes
of the reactive species. For a broad class of applications, these
methods are superior over Monte Carlo simulations.
The equations are linear, stable and converge fast, providing accurate
results without the need for statistical analysis of large sets of data.
Applications to interstellar chemistry and biological networks will be discussed.