Rovira Escofet, CarlesArmengol Collado, Josep-Maria2019-05-132019-05-132019-01-18https://hdl.handle.net/2445/133067Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Carles Rovira Escofet[en] We start by characterizing Brownian motion and giving its main properties, and then we focus on studying Itô’s and Stratonovich’s integral. We take special interest in comparing both perspectives and proving Wong-Zakai theorems, which connect stochastic and deterministic behaviour. Finally, it is also presented a brief introduction to stochastic differential equations, demonstrating a result for the existence and uniqueness of solutions.64 p.application/pdfengcc-by-nc-nd (c) Josep-Maria Armengol Collado, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/Moviment browniàTreballs de fi de grauProcessos estocàsticsIntegrals estocàstiquesEquacions diferencials estocàstiquesAnàlisi estocàsticaBrownian movementsBachelor's thesesStochastic processesStochastic integralsStochastic differential equationsAnalyse stochastiqueinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess