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Title

On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields

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Abstract

Let  {Xn,n∈Nd} 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 Nd   have been proved. Auxiliary lemmas have wider application to study  the random walks on the lattice.

Keywords

ENG
Baum-Katz type theorems, complete convergence, negatively dependent random fields, convergence of families indexed by directed sets, metric space

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Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
2018/72/2
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Main language of publication
English
Published
2018
Published online
2018-12-22

DOI: 10.17951/a.2018.72.2.1

Exact and natural sciences