A bound in the stable ($\alpha $), $1 < \alpha \le 2$, limit theorem for associated random variables with infinite variance

2021 ◽  
Vol 104 ◽  
pp. 145-156
Author(s):  
M. Sreehari
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Infinite Variance ◽  
Associated Random Variables

scholarly journals The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanying Jiang ◽  
Qunying Wu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Associated Sequences ◽  
Local Central Limit Theorem

In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables:limn→∞(1/logn)∑k=1n(I(ak≤Sk<bk)/k)P(ak≤Sk<bk)=1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central limit theorems from the i.i.d. case to the stationary negatively associated sequences.

scholarly journals Almost sure central limit theorems for strongly mixing and associated random variables

2002 ◽  
Vol 29 (3) ◽  
pp. 125-131 ◽  
Author(s):  
Khurelbaatar Gonchigdanzan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Mixing Rate ◽  
Associated Random Variables ◽  
Strongly Mixing ◽  
Slow Mixing ◽  
Mixing Sequence

We prove an almost sure central limit theorem (ASCLT) for strongly mixing sequence of random variables with a slightly slow mixing rateα(n)=O((loglogn)−1−δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.

scholarly journals Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1413-1422 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
The Self ◽  
Partial Sums ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

Let X,X1,X2,... be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the self-normalized partial sums Sn/Vn is established, where: Sn = ?ni=1 Xi,V2n = ?ni=1 X2i .

Some Generalized Central Limit Theorems for Weighted Sums with Infinite Variance

1989 ◽  
Vol 38 (1-2) ◽  
pp. 27-42 ◽  
Author(s):  
André Adler ◽  
Andrew Rosalsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Necessary Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Infinite Variance ◽  
Famous Result ◽  
Special Case

For i.i.d. random variables { Y, Yn, n⩾ 1} with EY2=∞ and nonzero constants { an, n⩾1}, sufficient and, separately, necessary conditions are given for { an Yn, n⩾1} to obey a generalized central limit theorem [Formula: see text] for suitable constants { An, n⩾1} and { Bn > 0, n⩾1}. The norming constants { Bn, n⩾1} are defined using the sequence [Formula: see text] and the distribution of Y. Moreover, it is shown that if p{| Y|> y} is regularly varying with exponent-2, then the centering constants may be taken to be [Formula: see text]. A famous result of Feller (1935), Khintchine (1935), and Lévy (1935) is obtained in the special case an ≡ 1.

Sign in / Sign up

Export Citation Format

Share Document