Exact Weak Laws and One Sided Strong Laws
André Adler · Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES · 2017
This paper explores Exact Weak Laws and their almost sure counterparts.First we show that the weighted sums of our infinite mean random variables can be balanced by a carefully selected sequence, i.e., that the ratio converges to one in probability.Then it is shown that the upper limit is almost surely infinity, while the lower limit is one. L(x+c j )x+c j