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Lp-calculus Approach to the Random Autonomous Linear Differential Equation with Discrete Delay
dc.contributor.author | Calatayud, Julia | |
dc.contributor.author | Cortés, Juan Carlos | |
dc.contributor.author | Jornet, Marc | |
dc.date.accessioned | 2022-11-25T18:30:54Z | |
dc.date.available | 2022-11-25T18:30:54Z | |
dc.date.issued | 2019-06-19 | |
dc.identifier.issn | 1660-5454 | |
dc.identifier.issn | 1660-5446 | |
dc.identifier.uri | http://hdl.handle.net/10234/200938 | |
dc.description.abstract | In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay τ > 0: x (t) = ax(t) + bx(t − τ ), t ≥ 0, with initial condition x(t) = g(t), −τ ≤ t ≤ 0. The coefficients a and b are assumed to be random variables, while the initial condition g(t) is taken as a stochastic process. Using Lp-calculus, we prove that, under certain conditions, the deterministic solution constructed with the method of steps that involves the delayed exponential function is an Lp-solution too. An analysis of Lp-convergence when the delay τ tends to 0 is also performed in detail. | ca_CA |
dc.format.extent | 17 p. | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Springer Nature Switzerland AG | ca_CA |
dc.relation | Programa de Ayudas de Investigación y Desarrollo (PAID) | ca_CA |
dc.relation.isPartOf | Mediterranean Journal of Mathematics, Vol. 16 (2019) | ca_CA |
dc.rights | © Springer Nature Switzerland AG 2019 | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | ca_CA |
dc.subject | random autonomous linear differential equation with discrete delay | ca_CA |
dc.subject | Lp random calculus | ca_CA |
dc.subject | method of steps | ca_CA |
dc.subject | uncertainty quantification | ca_CA |
dc.title | Lp-calculus Approach to the Random Autonomous Linear Differential Equation with Discrete Delay | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1007/s00009-019-1370-6 | |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | ca_CA |
dc.relation.publisherVersion | https://link.springer.com/article/10.1007/s00009-019-1370-6 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad (MINECO) | ca_CA |
project.funder.name | Universitat Politècnica de València | ca_CA |
oaire.awardNumber | MTM2017–89664–P | ca_CA |
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