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 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 Complete convergence for weighted sums of a class of random variables

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 509-522 ◽  
Author(s):  
Xin Deng ◽  
Meimei Ge ◽  
Xuejun Wang ◽  
Yanfang Liu ◽  
Yu Zhou
Keyword(s):  
Complete Convergence ◽  
Type Inequality ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Real Numbers ◽  
Mild Conditions ◽  
Rosenthal Type Inequality

Let {ani,1?i?n,n?1} be an array of real numbers and {Xn,n?1} be a sequence of random variables satisfying the Rosenthal type inequality, which is stochastically dominated by a random variable X. Under mild conditions, we present some results on complete convergence for weighted sums ?ni=1 aniXi of random variables satisfying the Rosenthal type inequality. The results obtained in the paper generalize some known ones in the literatures.

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 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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