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On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data
dc.contributor.author | Bevia, Vicente | |
dc.contributor.author | Calatayud, Julia | |
dc.contributor.author | Cortés, Juan Carlos | |
dc.contributor.author | Jornet, Marc | |
dc.date.accessioned | 2023-02-06T12:07:10Z | |
dc.date.available | 2023-02-06T12:07:10Z | |
dc.date.issued | 2022-08-27 | |
dc.identifier.citation | BEVIA, V., et al. On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data. Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 116, p. 106832. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/201547 | |
dc.description.abstract | Based on the previous literature about the random logistic and Gompertz models, the aim of this paper is to extend the investigations to the generalized logistic differential equation in the random setting. First, this is done by rigorously constructing its solution in two different ways, namely, the sample-path approach and the mean-square calculus. Secondly, the probability density function at each time instant is derived in two ways: by applying the random variable transformation technique and by solving the associated Liouville’s partial differential equation. It is also proved that both the stochastic solution and its density function converge, under specific conditions, to the corresponding solution and density function of the logistic and Gompertz models, respectively. The investigation finishes showing some examples, where a number of computational techniques are combined to construct reliable approximations of the probability density of the stochastic solution. In particular, we show, step-by-step, how our findings can be applied to a real-world problem. | ca_CA |
dc.format.extent | 17 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.relation.isPartOf | Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 116 | ca_CA |
dc.rights | © 2022 The Author(s). Published by Elsevier B.V. | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | ca_CA |
dc.subject | generalized logistic differential equation | ca_CA |
dc.subject | random differential equation | ca_CA |
dc.subject | sample-path and mean-square solution | ca_CA |
dc.subject | probability density function | ca_CA |
dc.subject | convergence | ca_CA |
dc.subject | real-world application | ca_CA |
dc.title | On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.cnsns.2022.106832 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Agencia Estatal de Investigación (AEI), Spain | ca_CA |
project.funder.name | Universitat Politècnica de València | ca_CA |
oaire.awardNumber | PID2020-115270GB-I00 | ca_CA |
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