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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/50066
- Gauge Poisson representations for birth/death master equations
- Drummond, P. D.
- 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.
- Publication type
- Journal article
- European Physical Journal B, Vol. 38, no. 4 (Apr 2004), pp. 617-634
- Publication year
- FOR Code(s)
- 0204 Condensed Matter Physics
- Boundary value problems; Computer simulation; Continuum mechanics; Correlation methods; Error analysis; Fokker-Planck equations; Genetics; Large scale systems; Linear rate equations; Markov processes; Mathematical models; Matrix algebra; Nonlinear equations; Parameter estimation; Poisson equation; Probability distributions; Problem solving; Quantum systems; Stochastic programming
- Publisher URL
- Copyright © 2004 EDP Sciences, Societa Italiana di Fisica, Springer-Verlag.
- Peer reviewed