dc.rights.license | Atribución-NoComercial 4.0 Internacional |
dc.contributor.advisor | Ramírez Osorio, Jorge Mario |
dc.contributor.author | Villa Cárdenas, Delsy Yurani |
dc.date.accessioned | 2020-05-26T20:32:27Z |
dc.date.available | 2020-05-26T20:32:27Z |
dc.date.issued | 2019-08-16 |
dc.identifier.citation | Y. Villa. Ecuaciones de Langevin en Coordenadas Polares. 2019 |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/77554 |
dc.description.abstract | In 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.abstract | En 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.sponsorship | HERMES |
dc.format.extent | 26 |
dc.format.mimetype | application/pdf |
dc.language.iso | spa |
dc.rights | Derechos reservados - Universidad Nacional de Colombia |
dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ |
dc.subject.ddc | 510 - Matemáticas |
dc.title | Ecuaciones de langevin en coordenadas polares |
dc.title.alternative | Langevin equations in polar coordinates |
dc.type | Otro |
dc.rights.spa | Acceso abierto |
dc.description.project | Formación espontánea de patrones geométricos en la dinámica de numerosos individuos móviles que se comunican mediante quimiotaxis |
dc.type.driver | info:eu-repo/semantics/other |
dc.type.version | info:eu-repo/semantics/acceptedVersion |
dc.publisher.program | Medellín - Ciencias - Maestría en Ciencias - Matemática Aplicada |
dc.contributor.corporatename | Universidad Nacional de Colombia |
dc.contributor.corporatename | Universidad Nacional de Colombia - Sede Medellín |
dc.contributor.researchgroup | Computación Científica |
dc.description.degreelevel | Maestría |
dc.publisher.department | Escuela de matemáticas |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Medellín |
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dc.rights.accessrights | info:eu-repo/semantics/openAccess |
dc.subject.proposal | Ecuación de Langevin |
dc.subject.proposal | Langevin Equation |
dc.subject.proposal | Coordenadas Polares |
dc.subject.proposal | Polar Coordinates |
dc.subject.proposal | Ecuaciones Diferenciales Estocásticas |
dc.subject.proposal | stochastic differential equations |
dc.subject.proposal | Distribución Invariante |
dc.subject.proposal | Invariant distribution |
dc.type.coar | http://purl.org/coar/resource_type/c_1843 |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa |
dc.type.content | Text |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |