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@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.