Lleis infinitament divisibles i processos de Lévy

Abstract

[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.