dorsal/arxiv
View SchemaGauge Poisson representations for birth/death master equations
| Authors | P. D. Drummond |
|---|---|
| Categories | |
| ArXiv ID | physics/0211061 |
| URL | https://arxiv.org/abs/physics/0211061 |
Abstract
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.
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"abstract": "Poisson representation techniques provide a powerful method for mapping\nmaster equations for birth/death processes -- found in many fields of physics,\nchemistry and biology -- into more tractable stochastic differential equations.\nHowever, the usual expansion is not exact in the presence of boundary terms,\nwhich commonly occur when the differential equations are nonlinear. In this\npaper, a gauge Poisson technique is introduced that eliminates boundary terms,\nto give an exact representation as a weighted rate equation with stochastic\nterms. These methods provide novel techniques for calculating and understanding\nthe effects of number correlations in systems that have a master equation\ndescription. As examples, correlations induced by strong mutations in genetics,\nand the astrophysical problem of molecule formation on microscopic grain\nsurfaces are analyzed. Exact analytic results are obtained that can be compared\nwith numerical simulations, demonstrating that stochastic gauge techniques can\ngive exact results where standard Poisson expansions are not able to.",
"arxiv_id": "physics/0211061",
"authors": [
"P. D. Drummond"
],
"categories": [
"physics.bio-ph",
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"physics.gen-ph",
"q-bio.PE",
"q-bio.QM"
],
"title": "Gauge Poisson representations for birth/death master equations",
"url": "https://arxiv.org/abs/physics/0211061"
},
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