Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7548946 | Statistics & Probability Letters | 2016 | 8 Pages |
Abstract
Let {X,Xn,nâ¥1} be a sequence of i.i.d. random variables with E[X]=0 and E[X2]=Ï2â(0,â), and set Sn=âk=1nXk,nâ¥1. For any δâ¥0, let γδ=limnââ(âj=1n(logj)δjâ(logn)δ+1δ+1)andηδ=ân=1â(logn)δnP(Sn=0). Under the moment condition E[X2(log(1+â£Xâ£))1+δ]<â, we prove that limϵâ0[ân=1â(logn)δnP(â£Snâ£â¥Ïµnlogn)âE[â£Nâ£2δ+2]δ+1Ï2δ+2ϵâ(2δ+2)]=γδâηδ, which refines Theorem 3 of Gut and SpÄtaru (2000a).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Lingtao Kong, Hongshuai Dai,