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Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions
dc.contributor.author | Calatayud, Julia | |
dc.contributor.author | Cortés, Juan Carlos | |
dc.contributor.author | Jornet, Marc | |
dc.date.accessioned | 2022-11-28T15:55:20Z | |
dc.date.available | 2022-11-28T15:55:20Z | |
dc.date.issued | 2019-07-16 | |
dc.identifier.citation | Calatayud, J., Cortes, J. C., & Jornet, M. (2019). Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions. | ca_CA |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | http://hdl.handle.net/10234/200964 | |
dc.description.abstract | Solving a random differential equation means to obtain an exact or approximate expression for the solution stochastic process, and to compute its statistical properties, mainly the mean and the variance functions. However, a major challenge is the computation of the probability density function of the solution. In this article we construct reliable approximations of the probability density function to the randomized non-autonomous complete linear differential equation by assuming that the diffusion coefficient and the source term are stochastic processes and the initial condition is a random variable. The key tools to construct these approximations are the random variable transformation technique and Karhunen-Lo`eve expansions. The study is divided into a large number of cases with a double aim: firstly, to extend the available results in the extant literature and, secondly, to embrace as many practical situations as possible. Finally, a wide variety of numerical experiments illustrate the potentiality of our findings. | ca_CA |
dc.format.extent | 40 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Texas State University | ca_CA |
dc.relation | Programa de Ayudas de Investigación y Desarrollo (PAID) | ca_CA |
dc.relation.isPartOf | Electronic Journal of Differential Equations, Vol. 2019, no. 85 (2019) | ca_CA |
dc.rights | © 2019 Texas State University | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | ca_CA |
dc.subject | random non-autonomous complete linear differential equation | ca_CA |
dc.subject | random variable transformation technique | ca_CA |
dc.subject | Karhunen-Loeve expansion | ca_CA |
dc.subject | probability density function | ca_CA |
dc.subject | 34F05 | ca_CA |
dc.subject | 60H35 | ca_CA |
dc.subject | 60H10 | ca_CA |
dc.subject | 65C30 | ca_CA |
dc.subject | 93E03 | ca_CA |
dc.title | Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://ejde.math.txstate.edu/ | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad | ca_CA |
project.funder.name | Universitat Politècnica de València | ca_CA |
oaire.awardNumber | MTM2017–89664–P | ca_CA |
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