El Món de les variables sense moments finits de tots els ordres: de la paradoxa de Sant Petersburg als processos de Lévy

Random variables without finite moments of all orders are not at present a
pathology, but a central subject in probability theory. From the Saint Petersburg
paradox, dated at the beginning of the eighteenth century, until the non-Gaussian
stable distributions and Lévy flights, a very beautiful theory has been
developed, at which, in this paper, we will take a quick glance. We will finish
with some applications to different situations as a taste of the importance
of this theory in mathematical modelling. Specifically, we will consider asset
prices modelling, the study of earthquakes, a new view to the classical Saint
Petersburg paradox, and finally the evolution of the mean temperature in the
North Atlantic sea over the last 250,000 years.