Ecuaciones de langevin en coordenadas polares

dc.contributor.advisorRamírez Osorio, Jorge Mariospa
dc.contributor.authorVilla Cárdenas, Delsy Yuranispa
dc.contributor.corporatenameUniversidad Nacional de Colombiaspa
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Medellínspa
dc.contributor.researchgroupComputación Científicaspa
dc.date.accessioned2020-05-26T20:32:27Zspa
dc.date.available2020-05-26T20:32:27Zspa
dc.date.issued2019-08-16spa
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..spa
dc.description.abstractEn 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 específicadaspa
dc.description.degreelevelMaestríaspa
dc.description.projectFormación espontánea de patrones geométricos en la dinámica de numerosos individuos móviles que se comunican mediante quimiotaxisspa
dc.description.sponsorshipHERMESspa
dc.format.extent26spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.citationY. Villa. Ecuaciones de Langevin en Coordenadas Polares. 2019spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/77554
dc.language.isospaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.departmentEscuela de matemáticasspa
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicadaspa
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dc.rightsDerechos reservados - Universidad Nacional de Colombiaspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial 4.0 Internacionalspa
dc.rights.spaAcceso abiertospa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.proposalEcuación de Langevinspa
dc.subject.proposalLangevin Equationeng
dc.subject.proposalCoordenadas Polaresspa
dc.subject.proposalPolar Coordinateseng
dc.subject.proposalEcuaciones Diferenciales Estocásticasspa
dc.subject.proposalstochastic differential equationseng
dc.subject.proposalDistribución Invariantespa
dc.subject.proposalInvariant distributioneng
dc.titleEcuaciones de langevin en coordenadas polaresspa
dc.title.alternativeLangevin equations in polar coordinatesspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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