A self-normalized law of the iterated logarithm for the geometrically weighted random series

Authors
Fu, Ke Ang Huang, Wei
Citation
Fu, Ke Ang et Huang, Wei, A self-normalized law of the iterated logarithm for the geometrically weighted random series, Acta mathematica Sinica. English series (Print) , 32(3), 2016, pp. 384-392
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
3
Year of publication
2016
Pages
384 - 392
Database
ACNP
SICI code
Abstract
Let {X,X n ; n . 0} be a sequence of independent and identically distributed random variables with EX = 0, and assume that EX 2 I(|X| . x) is slowly varying as x.., i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series ..n=0.nXn(0<.<1) is obtained, under some minimal conditions.