{"id":97383,"date":"2018-03-11T10:17:55","date_gmt":"2018-03-11T10:17:55","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/some-contributions-on-stochastic-partial-differential-equations-and-multiple-stochastic-integrals\/"},"modified":"2018-03-11T10:17:55","modified_gmt":"2018-03-11T10:17:55","slug":"some-contributions-on-stochastic-partial-differential-equations-and-multiple-stochastic-integrals","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/barcelona\/some-contributions-on-stochastic-partial-differential-equations-and-multiple-stochastic-integrals\/","title":{"rendered":"Some contributions on stochastic partial differential equations and multiple stochastic integrals"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Iv\u00e1n Torrecilla Tarantino <\/strong><\/h2>\n<p>En esta tesis doctoral se estudian tres problemas de an\u00e1lisis estoc\u00e1stico, dos sobre ecuaciones en derivadas parciales estoc\u00e1sticas y uno sobre integrales estoc\u00e1sticas multiples.   el primero de los problemas sobre ecuaciones en derivadas parciales estoc\u00e1sticas es una aplicaci\u00f3n cl\u00e1sica del c\u00e1lculo de malliavin. Concretamente, se estudia la existencia y regularidad de densidad para la ley de la soluci\u00f3n de una ecuaci\u00f3n diferencial estoc\u00e1stica en el plano con coeficientes no homog\u00e9neos y conducida por una manta browniana d-dimensional. Esta ecuaci\u00f3n corresponde a una ecuaci\u00f3n en derivadas parciales estoc\u00e1sticas hiperb\u00f3lica no lineal.   el segundo de los problemas sobre ecuaciones en derivadas parciales estoc\u00e1sticas consiste en probar la existencia y unicidad de soluci\u00f3n de una ecuaci\u00f3n en derivadas parciales estoc\u00e1stica el\u00edptica definida mediante el operador de laplace m\u00e1s un termino no lineal y con unas fuerzas externas dadas por un termino no aleatorio m\u00e1s un ruido fraccionario aditivo. Tambi\u00e9n se estudian algunas propiedades de las trayectorias mostrales de la soluci\u00f3n. Finalmente se dan esquemas en red utilizando el m\u00e9todo en diferencias finitas para dar una soluci\u00f3n num\u00e9rica de la soluci\u00f3n de la ecuaci\u00f3n estudiada y adem\u00e1s tambi\u00e9n se estudia la velocidad de convergencia de la aproximaci\u00f3n num\u00e9rica.  el \u00faltimo problema consiste en dar un principio de grandes desviaciones para integrales m\u00faltiples respecto del movimiento browniano fraccionario en el caso de que el par\u00e1metro de hurst sea ]1\/4,1\/2[u]1\/2,1[ y donde el integrando puede depender de un par\u00e1metro continuo. Adem\u00e1s el integrando es dado de tal forma que las trayectorias mostrales de estas integrales estoc\u00e1sticas m\u00faltiples pertenecen a un espacio de funciones h\u00ed\u00b6lder continuas concreto. Entonces para una familia de estas integrales estoc\u00e1sticas m\u00faltiples se da un principio de grandes desviaciones en la norma h\u00ed\u00b6lder.  finalmente, tambi\u00e9n se plantean algunos problemas abiertos para proseguir las investigaciones iniciadas a partir de esta tesis doctoral.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Some contributions on stochastic partial differential equations and multiple stochastic integrals<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Some contributions on stochastic partial differential equations and multiple stochastic integrals <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Iv\u00e1n Torrecilla Tarantino <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 23\/11\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Marta Sanz Sole<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Mar\u00eda Jolis gim\u00e9nez <\/li>\n<li>samy Tindel (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Iv\u00e1n Torrecilla Tarantino En esta tesis doctoral se estudian tres problemas de an\u00e1lisis estoc\u00e1stico, dos sobre ecuaciones [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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