Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2019). Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications. Mathematical Methods in the Applied Sciences. 42(17):5708-5717. https://doi.org/10.1002/mma.5440
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/139845
Title:
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Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications
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Author:
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Cortés, J.-C.
Navarro-Quiles, A.
Romero, José-Vicente
Roselló, María-Dolores
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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[EN] The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been ...[+]
[EN] The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.
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Subjects:
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First probability density function
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Modelling real data
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Pielou logistic equation
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Population dynamics
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Random difference stochastic equations
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Random variable transformation technique
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Mathematical Methods in the Applied Sciences. (issn:
0170-4214
)
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DOI:
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10.1002/mma.5440
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Publisher:
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John Wiley & Sons
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Publisher version:
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https://doi.org/10.1002/mma.5440
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Project ID:
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/
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Thanks:
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This work has been partially supported by the Ministerio de Economía y Competitividad grant MTM2017-89664-P
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Type:
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Artículo
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