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Exact Weak Laws and One Sided Strong Laws

Vol. 12 No. 2 (2017) P.103~P.124
 DOI: https://doi.org/10.21915/BIMAS.2017201 10.21915/BIMAS.2017201

ABSTRACT

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.

KEYWORDS
Almost sure convergence; weak law of large numbers; exact laws; one sided strong laws, slow variation.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F05, 60F15.

MILESTONES