Title: The convergence of sums of independent random variables under Peng's framework of sub-linear expectations

Speaker: Prof. Zhang Lixin(Zhejiang University)

Time: 15:30-16:30 May 17, 2019

Venue: B-1238 Zhixin Building

Abstract:

Under the classical framework of probability theory in which the probability measure and the expectation are additive, it is well-known that the almost sure convergence, the convergence in probability and the convergence in distribution of the infinite series of independent random variables are equivalent, and, the sufficient and necessary condition for the central limit theorem of independent and identically distributed random variables is that the second moment of the random variables is finite. In this talk, we show similar results under Peng's framework of sub-linear expectations. The inequalities for the tail capacity of maximum sums of independent random variables are established to show the results.