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 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 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)

IMPRECISE SECOND-ORDER MODEL FOR A SYSTEM OF INDEPENDENT RANDOM VARIABLES

2005 ◽  
Vol 13 (02) ◽  
pp. 177-193 ◽  
Author(s):  
LEV V. UTKIN
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Second Order ◽  
Independent Random Variables ◽  
Order Model ◽  
First Order ◽  
Probability Bounds ◽  
Uncertainty Model ◽  
Lower And Upper Probabilities ◽  
Interval Valued

A new hierarchical uncertainty model for combining different evidence about a system of statistically independent random variable is studied in the paper. It is assumed that the first-order level of the model is represented by sets of lower and upper previsions (expectations) of random variables and the second-order level is represented by sets of lower and upper probabilities which can be viewed as confidence weights for interval-valued expectations of the first-order level. The model is rather general and allows us to compute probability bounds and "average" bounds for previsions of a function of random variables. A numerical example illustrates this model.

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>

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