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

R. Vasudeva

Statistics & Probability Letters, 2018, vol. 137, issue C, 34-39

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.

Keywords: Semi-stable laws; Domain of partial attraction; Law of iterated logarithm; Almost sure limit function (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2017.12.003

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