Laws of large numbers for sequences and arrays of random variables

• Main Author: Tilahun, Gelila.
• Other Authors: Dion, J. P. (advisor)
• Format: Others
• Language: en
• Published: McGill University 1996
• Subjects: Statistics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27424

This thesis presents an up-to-date survey of results concerning laws of large numbers for sequences and arrays of random variables. We begin with Kolmogorov's pioneering result, the strong law of large numbers, and preceed through to Hu et al.'s, and Gut's recent result for weakly dominated random variables, for which we provide a simpler proof. We insist in particular on the techniques of proof of Etemadi and Jamison et al. Furthermore, analogues to the Marcinkiewicz-Zygmund theorem are given. This thesis illustrates the trade-off between the existence of higher moments and non i.i.d sequences and arrays of random variables to obtain the strong law of large numbers.