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| Format: | Artículo científico |
| Language: | en |
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Sociedade Brasileira de Física
2006
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| Online Access: | https://www.redalyc.org/articulo.oa?id=46436622 |
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| _version_ | 1866558093225099264 |
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| author | Nicholas R. Moloney |
| author_facet | Nicholas R. Moloney |
| contents | Functional-Integral Based Perturbation Theory for the Malthus-Verhulst Process Nicholas R. Moloney Ronald Dickman Física, Astronomía y Matemáticas and Birth Omega expansion death process We apply a functional-integral formalism for Markovian birth and death processes to determine asymptoticcorrections to mean-field theory in the Malthus-Verhulst process (MVP). Expanding about the stationary mean-field solution, we identify an expansion parameter that is small in the limit of large mean population, and derivea diagrammatic expansion in powers of this parameter. The series is evaluated to fifth order using computationalenumeration of diagrams. Although the MVP has no stationary state, we obtain good agreement with theassociated quasi-stationary values for the moments of the population size, provided the mean population size isnot small. We compare our results with those of van Kampens Ω-expansion, and apply our method to the MVPwith input, for which a stationary state does exist. We also devise a modified Fokker-Planck approach for thiscase. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436622 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| format | Artículo científico |
| id | redalyc_46436622 |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Functional-Integral Based Perturbation Theory for the Malthus-Verhulst Process Nicholas R. Moloney Física, Astronomía y Matemáticas and Birth Omega expansion death process Functional-Integral Based Perturbation Theory for the Malthus-Verhulst Process Nicholas R. Moloney Ronald Dickman Física, Astronomía y Matemáticas and Birth Omega expansion death process We apply a functional-integral formalism for Markovian birth and death processes to determine asymptoticcorrections to mean-field theory in the Malthus-Verhulst process (MVP). Expanding about the stationary mean-field solution, we identify an expansion parameter that is small in the limit of large mean population, and derivea diagrammatic expansion in powers of this parameter. The series is evaluated to fifth order using computationalenumeration of diagrams. Although the MVP has no stationary state, we obtain good agreement with theassociated quasi-stationary values for the moments of the population size, provided the mean population size isnot small. We compare our results with those of van Kampens Ω-expansion, and apply our method to the MVPwith input, for which a stationary state does exist. We also devise a modified Fokker-Planck approach for thiscase. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436622 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| title | Functional-Integral Based Perturbation Theory for the Malthus-Verhulst Process |
| topic | Física, Astronomía y Matemáticas and Birth Omega expansion death process |
| url | https://www.redalyc.org/articulo.oa?id=46436622 |