[Forum SIS] corso di Storia della Probabilità a Pavia

[Antonio Lijoi]

Nell'ambito delle attivita' del Dottorato di Ricerca in Matematica
(Universita' di Pavia - Universita' di Milano Bicocca - INdAM), il
prof. Eugenio Regazzini terra' il corso

** History of Probability in the First Half of XX Century **

Le lezioni (30 ore complessive) si terranno presso il Dipartimento di
Matematica "F. Casorati" dell'Universita' di Pavia, ogni giovedi' e
venerdi' dalle 10:00 alle 13:00, a partire dal 14 aprile.

Per ulteriori informazioni e' possibile contattare il docente via
email: eugenio.regazzini at unipv.it


** Descrizione del corso **
The first half of the last century has been a formidable period for
the development of probability and its applications. In point of fact,
during its course a number of open problems found a definitive answer
and, at the same time, sound bases towards new important achievements
were established.
The method adopted in the present course in order to illustrate the
advance of probability consists in analyzing the most original and
streamlined lines of reasoning to prove a certain number of theorems
generally seen as determining the magnificence of modern probability.
Since the aforesaid progress has been made possible even by the
axiomatization of probability, the first part of the course will be
devoted to this subject, drawing particular attention to the
foundational work of A. N. Kolmogorov (1933) and B. de Finetti (1931).
The second part will deal with distinguished versions of the strong
law of large number, starting from E. Borel (1909) and F.P. Cantelli
(1917), to get at the general formulation from the Soviet School
(Kolmogorov, A. Khinchin, etc.). In the case of stochastic
independence, their extensions to exchangeable random elements (de
Finetti), and more general stationary sequences (ergodic theorem of
von Neumann and Birkhoff) will be displayed and discussed. In this
very same part, the role played by stable and infinitely divisible
laws to solve the central limit problem (P. Lévy, Khinchin, W.
Doeblin, B. Gnedenko) will be emphasized. The last part will be
devoted to the birth of the theory of stochastic processes, starting
from the works of Kolmogorov (1929) on Markov processes, de Finetti
(1929 -1933) and Lévy (1934-1935) on random functions with independent
increments, Lévy (1935-1937) and J. Doob (1940) on martingales. This
last part will end with an outline to the methods devised in the
fifties to study convergence in law of stochastic processes.