Inequalities for the moments of sums of associated multi-indexed variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 417-425
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Exact upper bounds are obtained for absolute moments of order $r>2$ for finite sums of associated random variables forming a centered field on $\mathbf{N}^d$ or a countable set $T$. These estimates have the form $O(|V|^\tau)$ where $|V|$ is the number of summands. It is shown how the dependence of the summands and existence of their moments determine $\tau$.
Keywords:
association ($FKG$-inequality), random fields, sums of dependent random variables, inequalities for absolute moments of sums.
@article{TVP_1993_38_2_a10,
author = {A. V. Bulinski},
title = {Inequalities for the moments of sums of associated multi-indexed variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {417--425},
publisher = {mathdoc},
volume = {38},
number = {2},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a10/}
}
A. V. Bulinski. Inequalities for the moments of sums of associated multi-indexed variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 417-425. http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a10/