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On the random Gamma function: theory and computing

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On the random Gamma function: theory and computing

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dc.contributor.author Braunmann, C.A. es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Jódar Sánchez, Lucas Antonio es_ES
dc.contributor.author Villafuerte, Laura es_ES
dc.date.accessioned 2019-06-02T20:00:37Z
dc.date.available 2019-06-02T20:00:37Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121427
dc.description.abstract [EN] This paper deals with the extension, in the mean square sense, of the deterministic gamma function to the random framework. In a first step, we provide such extension to Gamma(A) by assuming that the parameter A is a positive random variable satisfying certain conditions related to its exponential moments. As a particular case, we show that every positive random variable satisfies such conditions if it is bounded and bounded away from zero. In a second step, we establish the formula Gamma(A + 1) = A Gamma(A) that allows us to extend the random gamma function to a class of random variables whose supports lie over the real line with the exception of small neighborhoods of zero and of the negative integers. This retains the classical definition of the gamma function when A becomes a deterministic parameter. The study is based on the L-P stochastic calculus with p = 2 and 4, usually referred to as mean square and mean fourth stochastic calculus, respectively. Next, we compute the mean and the variance of the random gamma function, including several illustrative examples. Finally, with the aid of the random gamma function, we define the random Bessel function and compute reliable approximations of its mean and variance. Published by Elsevier B.V. es_ES
dc.description.sponsorship This work has been partially supported by the Spanish M.C.Y.T. grant: MTM2013-41765-P and Mexican Conacyt. Carlos A. Braumann is a member of the Centro de Investigacao em Matematica e Aplicacoes (CIMA), Universidade de Evora, a research centre supported with Portuguese funds by FCT (Fundacao para a Ciencia e a Tecnologia, Portugal) through the Project UID/MAT/04674/2013. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation MINECO/MTM2013-41765-P es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Random gamma function es_ES
dc.subject Mean square stochastic calculus es_ES
dc.subject Mean fourth stochastic calculus es_ES
dc.subject Stochastic computations es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On the random Gamma function: theory and computing es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cam.2017.11.045 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/FCT/5876/147409/PT es_ES
dc.rights.accessRights Embargado es_ES
dc.date.embargoEndDate 2020-06-01 es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Braunmann, C.; Cortés, J.; Jódar Sánchez, LA.; Villafuerte, L. (2018). On the random Gamma function: theory and computing. Journal of Computational and Applied Mathematics. 335:142-155. https://doi.org/10.1016/j.cam.2017.11.045 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cam.2017.11.045 es_ES
dc.description.upvformatpinicio 142 es_ES
dc.description.upvformatpfin 155 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 335 es_ES
dc.relation.pasarela 348214 es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES
dc.contributor.funder Fundação para a Ciencia e a Tecnologia, Portugal


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