On the law of the iterated logarithm for a sequence of independent random variables

1995 ◽  
Vol 75 (5) ◽  
pp. 1958-1960
Author(s):  
V. V. Petrov
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Iterated Logarithm ◽  
The Law

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

scholarly journals On the laws of the iterated logarithm under sub-linear expectations

2021 ◽  
Vol 6 (4) ◽  
pp. 409
Author(s):  
Li-Xin Zhang
Keyword(s):  
Necessary Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Exponential Inequalities ◽  
Iterated Logarithm ◽  
Sufficient And Necessary Conditions ◽  
The Law ◽  
Independent And Identically Distributed

<p style='text-indent:20px;'>In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the iterated logarithm. As an application, the sufficient and necessary conditions of the law of the iterated logarithm for independent and identically distributed random variables under the sub-linear expectation are obtained. In the paper, it is also shown that if the sub-linear expectation space is rich enough, it will have no continuous capacity. The laws of the iterated logarithm are established without the assumption on the continuity of capacities.</p>

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.

Sign in / Sign up

Export Citation Format

Share Document