Stochastic differential equations driven by a fractional brownian motion
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Carles Rovira Escofet
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/216863 |
| Acceso en línea: | https://hdl.handle.net/2445/216863 |
| Access Level: | acceso abierto |
| Palabra clave: | Equacions diferencials estocàstiques Moviment brownià Treballs de fi de màster Stochastic differential equations Brownian movements Master's thesis |
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Stochastic differential equations driven by a fractional brownian motionBurés Mogollón, ÒscarEquacions diferencials estocàstiquesMoviment browniàTreballs de fi de màsterStochastic differential equationsBrownian movementsMaster's thesisTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Carles Rovira Escofet[en] This project is a general study of Stochastic Differential equations driven by a fractional Brownian motion of Hurst parameter $H>1 / 2$. Sections 3,4 and 5 follow the lines of [16] in order to define a stochastic integral with respect to the fractional Brownian motion and then, discussing the existence and uniqueness of solutions. The sixth section is a general discussion about Malliavin calculus with respect to the fractional Brownian motion that will be useful in sections 7 and 8 . Moreover, in section 6 we prove that by reinforcing the conditions on the coefficients, we obtain absolute continuity of the law of the solution in the same way as it is done in [14]. Section 7 is the application of the Malliavin calculus in order to bound the density function of the solution to a specific type of equations by using a general method constructed in [12]. Finally, section 8 is devoted to show all the work we weren't able to finish during the elaboration of this thesis. We decided to attack the problem of bounding the density of a general family of stochastic delay differential equations. The approach given in [12] turned out to be inefficient, so we decided to follow the same approach as in [1], [10] and [15].Rovira Escofet, Carles2024info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/216863Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Òscar Burés Mogollón, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2168632026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Stochastic differential equations driven by a fractional brownian motion |
| title |
Stochastic differential equations driven by a fractional brownian motion |
| spellingShingle |
Stochastic differential equations driven by a fractional brownian motion Burés Mogollón, Òscar Equacions diferencials estocàstiques Moviment brownià Treballs de fi de màster Stochastic differential equations Brownian movements Master's thesis |
| title_short |
Stochastic differential equations driven by a fractional brownian motion |
| title_full |
Stochastic differential equations driven by a fractional brownian motion |
| title_fullStr |
Stochastic differential equations driven by a fractional brownian motion |
| title_full_unstemmed |
Stochastic differential equations driven by a fractional brownian motion |
| title_sort |
Stochastic differential equations driven by a fractional brownian motion |
| dc.creator.none.fl_str_mv |
Burés Mogollón, Òscar |
| author |
Burés Mogollón, Òscar |
| author_facet |
Burés Mogollón, Òscar |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Rovira Escofet, Carles |
| dc.subject.none.fl_str_mv |
Equacions diferencials estocàstiques Moviment brownià Treballs de fi de màster Stochastic differential equations Brownian movements Master's thesis |
| topic |
Equacions diferencials estocàstiques Moviment brownià Treballs de fi de màster Stochastic differential equations Brownian movements Master's thesis |
| description |
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Carles Rovira Escofet |
| publishDate |
2024 |
| dc.date.none.fl_str_mv |
2024 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| format |
masterThesis |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/216863 |
| url |
https://hdl.handle.net/2445/216863 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.rights.none.fl_str_mv |
cc by-nc-nd (c) Òscar Burés Mogollón, 2024 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc by-nc-nd (c) Òscar Burés Mogollón, 2024 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
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Màster Oficial - Matemàtica Avançada reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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1869425779532627968 |
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15.811543 |