Vives i Santa Eulàlia, Josep, 1963-Piquer i Méndez, Marc2023-10-262023-10-262023-06-13https://hdl.handle.net/2445/203162Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Josep Vives i Santa Eulàlia[en] We study infinitely divisible distributions, which are the distributions of random variables which can be decomposed into $n$ other i.i.d. variables for all $n \in \mathbb{N}$, as well as the particular case of stable laws, and we give their representation by the Lévy-Khintchine theorem. We also study Lévy processes, the stochastically continuous stochastic processes with independent and stationary increments, which have a one-to-one correspondence with infinitely divisible distributions, and give their decomposition into continuous part and jump part known as the Lévy-Itô decomposition.53 p.application/pdfcatcc-by-nc-nd (c) Marc Piquer i Méndez, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Distribució (Teoria de la probabilitat)Processos estocàsticsProcessos de LévyTreballs de fi de grauDistribution (Probability theory)Stochastic processesLévy processesBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess