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Functional law of the iterated logarithm for partial sum processes of non-negative valued iid random variables belonging to the domain of partial attraction of a semi-stable law

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  • Vasudeva, R.

Abstract

Let (Xn) be a sequence of independent and identically distributed non-negative valued random variables defined over a common probability space and let F denote the common distribution function. Set Sn=X1+X2+⋯+Xn and denote inf{x;n(1−F(x))≤1} by Bn,n≥1. Assuming that F belongs to the domain of partial attraction of a positive semi-stable law, we obtain the set of almost sure limit functions of Bn−1S[nt]1loglogn,t∈[0,1], under M1-topology.

Suggested Citation

  • Vasudeva, R., 2018. "Functional law of the iterated logarithm for partial sum processes of non-negative valued iid random variables belonging to the domain of partial attraction of a semi-stable law," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 34-39.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:34-39
    DOI: 10.1016/j.spl.2017.12.003
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    1. Vasudeva, R. & Srilakshminarayana, G., 2013. "On strong large deviation results for lightly trimmed sums and some applications," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1745-1753.
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