ALMOST SURE MARCINKIEWICZ TYPE RESULT FOR THE ASYMPTOTICALLY NEGATIVELY DEPENDENT RANDOM FIELDS

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 4,  2009, pp.505-513
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.4.505
Title & Authors
ALMOST SURE MARCINKIEWICZ TYPE RESULT FOR THE ASYMPTOTICALLY NEGATIVELY DEPENDENT RANDOM FIELDS
Kim, Hyun-Chull;

Abstract
Let {$\small{X_k;k{\in}N^d}$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $\small{p{\alpha}}$ > 1 and $\small{{\alpha}}$ > $\small{{\frac{1}{2}}}$ $\small{E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})}$ < $\small{{\infty}}$ if and only if $\small{{\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P}$($\small{max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}}$ > $\small{{\epsilon}{\mid}n{\mid}}$) < $\small{{\infty}}$ for all $\small{{\epsilon}}$ > 0, where log$\small{^+}$x = max{1,log x}.
Keywords
asymptotically linear negative quadrant dependence;random field;identically distributed;complete convergence;maximal moment inequality;
Language
English
Cited by
References
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