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

• Autorzy: Zbigniew Łagodowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2018
• Tom: 72
• Numer: 2

Daty

wydano

2018

online

2018-12-22

Twórcy

autor

Zbigniew Łagodowski

Bibliografia

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Identyfikatory

DOI

10.17951/a.2018.72.2.1