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

Keynote Speaker: Zhang Lixin

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.

Speaker introduction:

Zhang Lixin is a Truth Seeking Specially-appointed Professor of Zhejiang University. He graduated from Fudan University with Doctor of Science degree in 1995, was promoted to be a professor in 1997, and worked successively as Deputy Director, Standing Deputy Director and Director of the Institute of Statistics Science of Zhejiang University from 2001 to 2012, as the Deputy Director of School of Mathematics of Zhejiang University from 2009 to 2015, and as the Associate Dean of School of Mathematical Science of Zhejiang University from 2015 to September 2017. He is now the Deputy Director of Center for Data Science of Zhejiang University, a member of IMS-China Committee, Managing Director of China Field Statistics Research Institute, Managing Director of Chinese Society of Probability and Statistics, and Chairman of Zhejiang Field Statistics Research Institute. He mainly engages in the research on probability limit theories, interdependent data models, stochastic self-adaption design in clinical test, and track quality characteristics in the stochastic process, etc., has published 160+ academic papers, and successively presided 5 NSFC projects and 1 key NSFC project. He was elected in "Zhejiang Trans-century 151 Talent Engineering" in 1998, and "New Century Outstanding Talent Support Plan" of the Ministry of Education in 2008, and won the fund for distinguished young scholars of Zhejiang Natural Science Foundation in 2010and the national science fund for distinguished young scholars of NSFC in 2012.

Inviter:

Wang Hanchao  Associate Professor

Time:

15:30-16:30, May 17 (Friday)

Location:

Hall 1238, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University