Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables

2005 ◽  
Vol 22 (3) ◽  
pp. 781-792 ◽  
Author(s):  
Ye Jiang ◽  
Li Xin Zhang
Keyword(s):  
Random Variables ◽  
Law Of Iterated Logarithm ◽  
Iterated Logarithm ◽  
The Law ◽  
The Moment

scholarly journals The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1313
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Independent Random Variable ◽  
Random Variables ◽  
Random Variable ◽  
Second Order ◽  
Law Of Iterated Logarithm ◽  
Independent Random Variables ◽  
Linear Processes ◽  
Iterated Logarithm ◽  
The Law

In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity.

scholarly journals The Law of Iterated Logarithm for Autoregressive Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yan Wang ◽  
Mingzhi Mao ◽  
Xiaohua Hu ◽  
Tingting He
Keyword(s):  
Least Squares ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Law Of Iterated Logarithm ◽  
Autoregressive Processes ◽  
Unknown Parameters ◽  
Iterated Logarithm ◽  
Ls Estimator ◽  
The Law

This paper mainly discusses some dynamics asymptotic properties of autoregressive processes. By using them-dependence of random variables, we prove the least squares (LS) estimator of the unknown parameters satisfies the law of iterated logarithm.

scholarly journals The law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality

2021 ◽  
Vol 6 (10) ◽  
pp. 11076-11083
Author(s):  
Haichao Yu ◽  
◽  
Yong Zhang
Keyword(s):  
Type Inequality ◽  
Random Variables ◽  
Random Variable ◽  
Law Of Iterated Logarithm ◽  
Variable Sequence ◽  
Iterated Logarithm ◽  
Rosenthal Type Inequality ◽  
The Law

<abstract><p>Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p &lt; \infty $ for each $ p &gt; 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.</p></abstract>

scholarly journals On the law of the iterated logarithm in the infinite variance case

1980 ◽  
Vol 30 (1) ◽  
pp. 5-14 ◽  
Author(s):  
R. A. Maller
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Infinite Variance ◽  
Iterated Logarithm ◽  
The Law ◽  
Necessary And Sufficient ◽  
Independent And Identically Distributed

AbstractThe main purpose of the paper is to give necessary and sufficient conditions for the almost sure boundedness of (Sn – αn)/B(n), where Sn = X1 + X2 + … + XmXi being independent and identically distributed random variables, and αnand B(n) being centering and norming constants. The conditions take the form of the convergence or divergence of a series of a geometric subsequence of the sequence P(Sn − αn > a B(n)), where a is a constant. The theorem is distinguished from previous similar results by the comparative weakness of the subsidiary conditions and the simplicity of the calculations. As an application, a law of the iterated logarithm general enough to include a result of Feller is derived.

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