Study of stochastic differential equations driven by fractional brownian motion

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: David Márquez

Detalhes bibliográficos
Autor: Serrat i Castella, Abel
Formato: tesis de maestría
Fecha de publicación:2023
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/202220
Acesso em linha:https://hdl.handle.net/2445/202220
Access Level:acceso abierto
Palavra-chave:Integrals estocàstiques
Equacions diferencials estocàstiques
Treballs de fi de màster
Stochastic integrals
Stochastic differential equations
Master's thesis
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spelling Study of stochastic differential equations driven by fractional brownian motionSerrat i Castella, AbelIntegrals estocàstiquesEquacions diferencials estocàstiquesTreballs de fi de màsterStochastic integralsStochastic differential equationsMaster's thesisTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: David Márquez[en] In this thesis we study and develop in detail the research paper Differential equations driven by fractional brownian motion by D. Nualart and A. Rascanu, 7]. It is a landmark paper in which the authors prove the existence and uniqueness of solution to stochastic differential equations driven by fractional Brownian motion of Hurst parameter $H \in(1 / 2,1)$. Moreover, they show that, under additional hypothesis, the solution has finite moments of all orders. They take a path-by-path approach given the Hölder-continuity property of the paths of the fractional Brownian motion. On our part, after a gentle introduction to the fractional integrals and derivatives and to the generalized Stieltjes integral, we fully develop the results and proofs of this paper. Not only that but we insert our own remarks and comment on the obtained results regarding the measurability of the solution. As a result, this thesis could be considered a companion paper intended to the reader interested in this important result but not versed in the foundations of stochastic differential equations.Márquez, David (Márquez Carreras)2023info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/202220Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Abel Serrat i Castella, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2022202026-05-27T06:46:51Z
dc.title.none.fl_str_mv Study of stochastic differential equations driven by fractional brownian motion
title Study of stochastic differential equations driven by fractional brownian motion
spellingShingle Study of stochastic differential equations driven by fractional brownian motion
Serrat i Castella, Abel
Integrals estocàstiques
Equacions diferencials estocàstiques
Treballs de fi de màster
Stochastic integrals
Stochastic differential equations
Master's thesis
title_short Study of stochastic differential equations driven by fractional brownian motion
title_full Study of stochastic differential equations driven by fractional brownian motion
title_fullStr Study of stochastic differential equations driven by fractional brownian motion
title_full_unstemmed Study of stochastic differential equations driven by fractional brownian motion
title_sort Study of stochastic differential equations driven by fractional brownian motion
dc.creator.none.fl_str_mv Serrat i Castella, Abel
author Serrat i Castella, Abel
author_facet Serrat i Castella, Abel
author_role author
dc.contributor.none.fl_str_mv Márquez, David (Márquez Carreras)
dc.subject.none.fl_str_mv Integrals estocàstiques
Equacions diferencials estocàstiques
Treballs de fi de màster
Stochastic integrals
Stochastic differential equations
Master's thesis
topic Integrals estocàstiques
Equacions diferencials estocàstiques
Treballs de fi de màster
Stochastic integrals
Stochastic differential equations
Master's thesis
description Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: David Márquez
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/202220
url https://hdl.handle.net/2445/202220
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-nd (c) Abel Serrat i Castella, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Abel Serrat i Castella, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418803946848256
score 15,300719

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