A Spitzer-type law of large numbers for widely orthant dependent random variables

Pingyan Chen and Soo Hak Sung

Statistics & Probability Letters, 2019, vol. 154, issue C, -

Abstract: It is well known that, for a sequence of independent and identically distributed random variables {X,Xn,n≥1},EX=0 implies ∑n=1∞n−1P(max1≤k≤n|Sk|>εn)<∞,∀ε>0 (Spitzer’s law), where Sn=X1+⋯+Xn. In this paper, we extend the result to widely orthant dependent random variables.

Keywords: Spitzer’s law of large numbers; Widely orthant dependent random variables; Extended negatively dependent random variables (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.06.020

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