Let be a random field of negatively dependent random variables. The complete convergence results for negatively dependent random fields are refined. To obtain the main theorem several lemmas for convergence of families indexed by have been proved. Auxiliary lemmas have wider application to study the random walks on the lattice.
@article{bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_1,
author = {Zbigniew \L agodowski},
title = {On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {72},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_1}
}
Zbigniew Łagodowski. On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 72 (2018) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_1/
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