Stochastic population dynamics: the Poisson approximation
We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorpt...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15393755_v67_n3_p031918_Solari |
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todo:paper_15393755_v67_n3_p031918_Solari2023-10-03T16:22:03Z Stochastic population dynamics: the Poisson approximation Solari, H.G. Natiello, M.A. Monte Carlo method Poisson distribution population dynamics Monte Carlo Method Poisson Distribution Population Dynamics We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v67_n3_p031918_Solari |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Monte Carlo method Poisson distribution population dynamics Monte Carlo Method Poisson Distribution Population Dynamics |
| spellingShingle |
Monte Carlo method Poisson distribution population dynamics Monte Carlo Method Poisson Distribution Population Dynamics Solari, H.G. Natiello, M.A. Stochastic population dynamics: the Poisson approximation |
| topic_facet |
Monte Carlo method Poisson distribution population dynamics Monte Carlo Method Poisson Distribution Population Dynamics |
| description |
We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics. |
| format |
JOUR |
| author |
Solari, H.G. Natiello, M.A. |
| author_facet |
Solari, H.G. Natiello, M.A. |
| author_sort |
Solari, H.G. |
| title |
Stochastic population dynamics: the Poisson approximation |
| title_short |
Stochastic population dynamics: the Poisson approximation |
| title_full |
Stochastic population dynamics: the Poisson approximation |
| title_fullStr |
Stochastic population dynamics: the Poisson approximation |
| title_full_unstemmed |
Stochastic population dynamics: the Poisson approximation |
| title_sort |
stochastic population dynamics: the poisson approximation |
| url |
http://hdl.handle.net/20.500.12110/paper_15393755_v67_n3_p031918_Solari |
| work_keys_str_mv |
AT solarihg stochasticpopulationdynamicsthepoissonapproximation AT natielloma stochasticpopulationdynamicsthepoissonapproximation |
| _version_ |
1782030253813661696 |