Ecuaciones de langevin en coordenadas polares
dc.contributor.advisor | Ramírez Osorio, Jorge Mario | spa |
dc.contributor.author | Villa Cárdenas, Delsy Yurani | spa |
dc.contributor.corporatename | Universidad Nacional de Colombia | spa |
dc.contributor.corporatename | Universidad Nacional de Colombia - Sede Medellín | spa |
dc.contributor.researchgroup | Computación Científica | spa |
dc.date.accessioned | 2020-05-26T20:32:27Z | spa |
dc.date.available | 2020-05-26T20:32:27Z | spa |
dc.date.issued | 2019-08-16 | spa |
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.. | spa |
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 | spa |
dc.description.degreelevel | Maestría | spa |
dc.description.project | Formación espontánea de patrones geométricos en la dinámica de numerosos individuos móviles que se comunican mediante quimiotaxis | spa |
dc.description.sponsorship | HERMES | spa |
dc.format.extent | 26 | spa |
dc.format.mimetype | application/pdf | spa |
dc.identifier.citation | Y. Villa. Ecuaciones de Langevin en Coordenadas Polares. 2019 | spa |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/77554 | |
dc.language.iso | spa | spa |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Medellín | spa |
dc.publisher.department | Escuela de matemáticas | spa |
dc.publisher.program | Medellín - Ciencias - Maestría en Ciencias - Matemática Aplicada | spa |
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dc.relation.references | A. Perna, B. Granovskiy, S. Garnier, S. C. Nicolis, M. Labédan, G. Theraulaz, V. Fourcassié, and D.J. Sumpter. Individual rules for trail pattern formation in Argentine ants (linepithema humile). PLoS Computational Biology, 8(7), 2012. | spa |
dc.relation.references | D. Revuz and M. Yor. Continuous Martingales and Brownian Motion, volume 293. 1999. | spa |
dc.relation.references | P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier. Active Brownian Particles. From Individual to Collective Stochastic Dynamics. 2012. | spa |
dc.relation.references | M. Schienbein and H. Gruler. Langevin equation, Fokker-Planck equation and cell migration. Bulletin of Mathematical Biology, 55(3):585-608, 1993. | spa |
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dc.rights | Derechos reservados - Universidad Nacional de Colombia | spa |
dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
dc.rights.license | Atribución-NoComercial 4.0 Internacional | spa |
dc.rights.spa | Acceso abierto | spa |
dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | spa |
dc.subject.ddc | 510 - Matemáticas | spa |
dc.subject.proposal | Ecuación de Langevin | spa |
dc.subject.proposal | Langevin Equation | eng |
dc.subject.proposal | Coordenadas Polares | spa |
dc.subject.proposal | Polar Coordinates | eng |
dc.subject.proposal | Ecuaciones Diferenciales Estocásticas | spa |
dc.subject.proposal | stochastic differential equations | eng |
dc.subject.proposal | Distribución Invariante | spa |
dc.subject.proposal | Invariant distribution | eng |
dc.title | Ecuaciones de langevin en coordenadas polares | spa |
dc.title.alternative | Langevin equations in polar coordinates | spa |
dc.type | Trabajo de grado - Maestría | spa |
dc.type.coar | http://purl.org/coar/resource_type/c_bdcc | spa |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | spa |
dc.type.content | Text | spa |
dc.type.driver | info:eu-repo/semantics/masterThesis | spa |
dc.type.version | info:eu-repo/semantics/acceptedVersion | spa |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |
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