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

Zbigniew Łagodowski

Abstract


Let  \(\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}\) 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 \(\mathbb{N}^d\)   have been proved. Auxiliary lemmas have wider application to study  the random walks on the lattice.

Keywords


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

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References


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DOI: http://dx.doi.org/10.17951/a.2018.72.2.1
Date of publication: 2018-12-22 22:03:10
Date of submission: 2018-12-21 13:00:51


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