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dc.rights.licenseAtribución-NoComercial 4.0 Internacional
dc.contributor.advisorRamírez Osorio, Jorge Mario
dc.contributor.authorVilla Cárdenas, Delsy Yurani
dc.identifier.citationY. Villa. Ecuaciones de Langevin en Coordenadas Polares. 2019
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.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 específicada
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.subject.ddc510 - Matemáticas
dc.titleEcuaciones de langevin en coordenadas polares
dc.title.alternativeLangevin equations in polar coordinates
dc.rights.spaAcceso abierto
dc.description.projectFormación espontánea de patrones geométricos en la dinámica de numerosos individuos móviles que se comunican mediante quimiotaxis
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicada
dc.contributor.corporatenameUniversidad Nacional de Colombia
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Medellín
dc.contributor.researchgroupComputación Científica
dc.publisher.departmentEscuela de matemáticas
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellín
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dc.subject.proposalEcuación de Langevin
dc.subject.proposalLangevin Equation
dc.subject.proposalCoordenadas Polares
dc.subject.proposalPolar Coordinates
dc.subject.proposalEcuaciones Diferenciales Estocásticas
dc.subject.proposalstochastic differential equations
dc.subject.proposalDistribución Invariante
dc.subject.proposalInvariant distribution

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Atribución-NoComercial 4.0 InternacionalThis work is licensed under a Creative Commons Reconocimiento-NoComercial 4.0.This document has been deposited by the author (s) under the following certificate of deposit