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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Detalles Bibliográficos
Autores principales:	Solari, Hernán Gustavo, Natiello, Mario Alberto
Publicado:	2003
Materias:	Monte Carlo method Poisson distribution population dynamics Monte Carlo Method Poisson Distribution Population Dynamics
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v67_n3_p031918_Solari http://hdl.handle.net/20.500.12110/paper_15393755_v67_n3_p031918_Solari
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v67_n3_p031918_Solari
record_format	dspace
spelling	paper:paper_15393755_v67_n3_p031918_Solari2023-06-08T16:20:23Z Stochastic population dynamics: the Poisson approximation Solari, Hernán Gustavo Natiello, Mario Alberto 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. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v67_n3_p031918_Solari 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, Hernán Gustavo Natiello, Mario Alberto 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.
author	Solari, Hernán Gustavo Natiello, Mario Alberto
author_facet	Solari, Hernán Gustavo Natiello, Mario Alberto
author_sort	Solari, Hernán Gustavo
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
publishDate	2003
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v67_n3_p031918_Solari http://hdl.handle.net/20.500.12110/paper_15393755_v67_n3_p031918_Solari
work_keys_str_mv	AT solarihernangustavo stochasticpopulationdynamicsthepoissonapproximation AT natiellomarioalberto stochasticpopulationdynamicsthepoissonapproximation
_version_	1768543200316751872

Stochastic population dynamics: the Poisson approximation

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