Márquez, David (Márquez Carreras)Suñé Margineda, Joel2020-06-222020-06-222020-01-19https://hdl.handle.net/2445/166399Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: David Márquez Carreras[en] The aim of this project is to study the Brownian motion highlighting its importance in relation to other more general stochastic processes. In the first place, the movement is rigorously defined and its existence is proven through a construction of the process (the Lévy-Ciesielski construction). And secondly, the properties of its sample-paths, as well as its characteristics as a martingale and a Markov process, are analyzed in detail.48 p.application/pdfcatcc-by-nc-nd (c) Joel Suñé Margineda, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Moviment browniàTreballs de fi de grauProcessos gaussiansMartingales (Matemàtica)Brownian movementsBachelor's thesesGaussian processesMartingales (Mathematics)info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess