Exact strong laws of large numbers for independent random fields
Volume 66 / 2018
Bulletin Polish Acad. Sci. Math. 66 (2018), 179-188
MSC: Primary 60F15; Secondary 60G60.
DOI: 10.4064/ba8153-9-2018
Published online: 19 October 2018
Abstract
Let be a family of independent random variables with multidimensional indices (a random field) with the same distribution as the r.v. X. A necessary and sufficient condition for the strong law of large numbers in this setting is \mathbb E \vert X\vert \log _{+}^{d-1}\vert X\vert \lt \infty. Our goal is to study the almost sure convergence of normalized or weighted sums in the case when this moment condition is not satisfied.
