Wenbo V. Li

Title: Recent Advances in Chung's LIL (Not the Other LIL)

Abstract: This is an expended version of a presentation in memory of Kai-Lai Chung in a special session on Seminar on Stochastic Processes 2010 (SSP10) held on March 11-13, 2010 at the University of Central Florida in Orlando. The original title of the talk is ``Chung's LIL (Not the Other LIL)''. Chung's LIL (and the associated small value probability estimate) was established in his Ph.D. thesis from Princeton University in 1947 under H. Cramer (officially signed by J. Tukey and Wilks) and appeared in the paper (the most cited paper of K-L Chung based on Math Review): Chung, Kai Lai, On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. Vol 64, 205--233, (1948). Those who had the most influence on Chung's thesis work are, in order of significance as Chung discussed in his thesis and paper, H. Cramer, W. Feller, Erdos and Hunt. We first present key ingredients in his seminal contribution and then discuss significant progresses in the 1960's, often called the other LIL. Recent advances and connections associated with small ball/deviation/value probabilities are reviewed and discussed.
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    Last modified Oct. 10, 2010 by Wenbo V. Li,