Cortés, J.; Jódar Sánchez, LA.; Company Rossi, R.; Villafuerte, L. (2015). Laguerre random differential polynomials: definition, differential and statistical properties. Utilitas Mathematica. 98:283-293. http://hdl.handle.net/10251/73814
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/73814
Title:
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Laguerre random differential polynomials: definition, differential and statistical properties
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Author:
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Cortés, J.-C.
Jódar Sánchez, Lucas Antonio
Company Rossi, Rafael
Villafuerte, Laura
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UPV Unit:
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Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports
Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses
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Issued date:
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Abstract:
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[EN] In this paper we introduce the Laguerre polynomials as mean square solutions of random differential equations. The study is based on the construction of an infinite random power series solution which becomes a random ...[+]
[EN] In this paper we introduce the Laguerre polynomials as mean square solutions of random differential equations. The study is based on the construction of an infinite random power series solution which becomes a random polynomial under certain conditions to be satisfied by the single involved random coefficient, denoted by A. This approach allows us to introduce the concept of Laguerre polynomials associated to the random variable A retaining their deterministic definition when the probability mass of A is concentrated in a nonnegative integer. As a result, we provide a natural way to extend the deterministic Laguerre polynomials to the random framework. In addition, the main statistical functions of the approximate solution stochastic process obtained by truncation of the exact power series solution, which generates random Laguerre polynomials, are also given. Several illustrative examples are provided.
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Subjects:
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Laguerre random polynomials
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Random differential equation
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Mean square calculus
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Mean fourth calculus.
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Utilitas Mathematica. (issn:
0315-3681
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Publisher:
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University of Manitoba - Department of Computer Science
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Project ID:
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MCYT/MTM2009-08587
UPV/PAID06-11-2070
MCYT/DPI2010-20891-C02-01
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Thanks:
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This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-05857, DPI2010-20891-C02-01, Universitat Politècnica de València grant PAID06-11-2070 and Mexican CONACYT
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Type:
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Artículo
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