Probability in Banach Spaces at Saint-Flour

Founded in 1971, the Saint-Flour Probability Summer School is organised every year by the mathematics department of the Université Blaise Pascal at Clermont-Ferrand, France, and held in the pleasant surroundings of an 18th century seminary building in the city of Saint-Flour, located in the French Massif Central, at an altitude of 900 m.It attracts a mixed audience of up to 70 PhD students, instructors and researchers interested in probability theory, statistics, and their applications, and lasts 2 weeks. Each summer it provides, in three high-level courses presented by international specialists, a comprehensive study of some subfields in probability theory or statistics. The participants thus have the opportunity to interact with these specialists and also to present their own research work in short lectures.The lecture courses are written up by their authors for publication in the LNM series.

Prolegomenes au calcul des probabilités dans les Banach.- Régularité des trajectoires des fonctions aléatoires Gaussiennes.- Probability in Banach space.- The law of the iterated logarithm and related strong convergence theorems for Banach space valued random variables.