Cun-Hui Zhang
Rutgers University
Title: Strong law of larg numbers for variables with infinite moments..

Let S_n be partial sums of i.i.d. variables from X. Suppose E(X)=0 whenever E(|X|) is finite. For 0 < p < 2, the Marcinkiewicz-Zygmund strong law of large numbers (SLLN) asserts that E(|X|^p) is finite iff S_n n^{-1/p} converges to zero almost surely. If E(|X|^p) is infinite, what is the almost sure upper limit of S_n n^{-1/p} ?
©2004, Department of Mathematical Sciences
Last Modified: May 16, 2005