On behalf of the Scientific Committee of the "B. de Finetti Risk Seminars, Milano Lectures on the Mathematical Theory of Economics and Finance”, we are glad to invite you to participate at the following Lecture on October 13, 2025 at 18:00: 

Walter Schachermayer, University of Vienna

LOCATION

Seminar Room 3-E4-SR03, Bocconi University, Milano

Title: Lacunary/Hereditary Limit Theorems in Probability and Analysis

Abstract: J. Komlos proved in 1967 an extremely useful theorem. For any bounded sequence (f_n) in L^1 there is a subsequence n_k and a limiting function f such that f_{n_k} converges to f almost surely in Cesaro mean. The convergence not only holds for the subsequence f_{n_k}, but also for each of its sub-subsequences. This important result may be seen as an extension of the strong law of large numbers, pertaining to arbitrarily dependent sequences of random variables. We analyze also other lacunary/hereditary versions of classical variants of the law of large numbers. Special attention will be given to the law of large numbers of Hsu-Robbins-Erdös from 1947/49. We show that it is indispensable for the proof of a lacunary/hereditary version of this theorem to use approximations by exchangeable sequences of random variables (as opposed to martingale differences). This yields the first example verifying a conjecture by D. Aldous from 1977.

Scientific Committee 

Prof. Simone Cerreia-Voglio (Univ. Bocconi) 

Prof. Marco Frittelli (Univ. degli Studi di Milano) 

Prof. Fabio Maccheroni (Univ. Bocconi)

Prof. Marco Maggis (Univ. degli Studi di Milano) 

Prof. Massimo Marinacci (Univ. Bocconi) 

Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca)