Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process

2008 ◽  
Vol 78 (9) ◽  
pp. 1051-1055 ◽  
Author(s):  
Yong Zhang ◽  
Xiao-Yun Yang
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.


2000 ◽  
Vol 28 (4) ◽  
pp. 1870-1883 ◽  
Author(s):  
Allan Gut ◽  
Aurel Spătaru

2014 ◽  
Vol 2014 (1) ◽  
pp. 137
Author(s):  
Tian-Xiao Pang ◽  
Zheng-Yan Lin ◽  
Kyo-Shin Hwang

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Junshan Xie ◽  
Lin He

Let{ξi,1≤i≤n}be a sequence of iidU[0, 1]-distributed random variables, and define the uniform empirical processFn(t)=n-1/2∑i=1n‍(I{ξi≤t}-t),0≤t≤1,Fn=sup0≤t≤1|Fn(t)|. When the nonnegative functiong(x)satisfies some regular monotone conditions, it proves thatlimϵ↘0⁡1/-logϵ∑n=1∞g′(n)/g(n)E{Fn2I{∥Fn∥≥ϵg(n)}}=π2/6.


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