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

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  • Chen, Pingyan
  • Sung, Soo Hak

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.

Suggested Citation

  • Chen, Pingyan & Sung, Soo Hak, 2019. "A Spitzer-type law of large numbers for widely orthant dependent random variables," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:9
    DOI: 10.1016/j.spl.2019.06.020
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    References listed on IDEAS

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    1. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    2. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
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