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Precise Asymptotics in Wichura's Law of Iterated Logarithm

Abstract

Gooty Divanji*, Kokkada Vidyalaxmi and K. N. Raviprakash

Let fXn; n  1g be a sequence of independent and identically distributed random variables with a common distribution
function F = P(X  x) in the domain of attraction of a asymmetric stable law, with index , 1 <  < 2 and set
Sn =
Pn
k=1
Xk. We prove that,
lim
"!0
p
"
X
n3
1
n
P (Sn  (  

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