Gauge Poisson representations for birth/death master equations
Universität Erlangen-Nürnberg, Lehrstuhl für Optik, Staudstrasse 7/B2 91058 Erlangen, Germany
Corresponding author: a email@example.com
Revised: 12 February 2004
Published online: 8 June 2004
Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes — found in many fields of physics, chemistry and biology — into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 95.30.Ft – Molecular and chemical processes and interactions / 87.23.Kg – Dynamics of evolution
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004