@TechReport{ it:2007-011,
author = {Lars Ferm and Per L{\"o}tstedt and Andreas Hellander},
title = {A Hierarchy of Approximations of the Master Equation
Scaled by a Size Parameter},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2007},
number = {2007-011},
month = apr,
abstract = {Solutions of the master equation are approximated using a
hierarchy of models based on the solution of ordinary
differential equations: the macroscopic equations, the
linear noise approximation and the moment equations. The
advantage with the approximations is that the computational
work with deterministic algorithms grows as a polynomial in
the number of species instead of an exponential growth with
conventional methods for the master equation. The relation
between the approximations is investigated theoretically
and in numerical examples. The solutions converge to the
macroscopic equations when a parameter measuring the size
of the system grows. A computational criterion is suggested
for estimating the accuracy of the approximations. The
numerical examples are models for the migration of people,
in population dynamics and in molecular biology.}
}