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dc.contributor.advisorRamírez Osorio, Jorge Mario
dc.creatorVilla Cárdenas, Delsy Yurani
dc.date.accessioned2020-05-26T20:32:27Z
dc.date.available2020-05-26T20:32:27Z
dc.date.created2019-08-16
dc.identifier.citationY. Villa. Ecuaciones de Langevin en Coordenadas Polares. 2019
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/77554
dc.descriptionEn la primera parte de este trabajo utilizamos la caracterización de Levy del movimiento Browniano y un teorema de cambio temporal para Martingales para deducir las ecuaciones diferenciales estocásticas que describen los procesos radial y angular de un proceso bidimensional de Ornstein-Uhlenbeck. En la segunda parte demostramos la existencia y unicidad del proceso radial de Ornstein-Uhlenbeck y analizamos la viabilidad de usar esta ecuación en la modelación. Finalmente, se muestra que la distribución del proceso radial de Ornstein-Uhlenbeck converge a una distribución invariante con una media y varianza específicada
dc.description.abstractIn the first part of this work we use Levy's characterization of Brownian motion and a Time-Change theorem for Martingales to deduce the stochastic differential equations that describe the radial and angular processes of a two-dimensional Ornstein-Uhlenbeck process. In the second part we demonstrate the existence and uniqueness of the radial Ornstein-Uhlenbeck process and analyze its usefulness for modeling. Finally, we show that the distribution of the radial Ornstein-Uhlenbeck process converges to an invariant distribution with an specified mean and variance..
dc.description.sponsorshipHERMES
dc.format.extent26
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/
dc.subjectEcuación de Langevin
dc.subjectCoordenadas Polares
dc.subjectEcuaciones Diferenciales Estocásticas
dc.subjectDistribución Invariante
dc.subject.ddc510 - Matemáticas
dc.titleEcuaciones de langevin en coordenadas polares
dc.title.alternativeLangevin equations in polar coordinates
dc.typeOther
dc.rights.spaAcceso abierto
dc.contributor.institutionUniversidad Nacional de Colombia - Sede Medellín
dc.subject.keywordLangevin Equation
dc.subject.keywordPolar Coordinates
dc.subject.keywordstochastic differential equations
dc.subject.keywordInvariant distribution
dc.type.spaOtro
dc.type.hasversionAccepted Version
dc.coverage.programEscuela de matemáticas
dc.contributor.gruplacComputación Científica
dc.description.projectFormación espontánea de patrones geométricos en la dinámica de numerosos individuos móviles que se comunican mediante quimiotaxis
dc.coverage.modalityMaestria
dc.rights.accessRightsOpen Access
dc.rights.ccCC0 1.0 Universal
dc.contributor.corpauthorUniversidad Nacional de Colombia
dc.contributor.corpauthorUniversidad Nacional de Colombia - Sede Medellín
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dc.contributor.generoFemenino
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicada


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