Gauge Poisson representations for birth/death master equations

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dc.creatorDrummond, P. D.
dc.date2002-11-14
dc.date2004-05-11
dc.date.accessioned2026-07-07T05:48:26Z
dc.date.available2026-07-07T05:48:26Z
dc.descriptionPoisson 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.
dc.descriptionVersion accepted for publication in European Physical Journal B
dc.identifierhttps://arxiv.org/abs/physics/0211061
dc.identifierhttp://arxiv.org/abs/physics/0211061
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/85023
dc.subjectBiological Physics
dc.subjectAstrophysics
dc.subjectGeneral Physics
dc.subjectPopulations and Evolution
dc.subjectQuantitative Methods
dc.titleGauge Poisson representations for birth/death master equations
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