Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables

2011 ◽  
Vol 217 (23) ◽  
pp. 9598-9605 ◽  
Author(s):  
Dah-Yan Hwang
Keyword(s):  
Random Variables ◽  
Higher Moments ◽  
Convex Mapping ◽  
Trapezoidal Formula ◽  
Moments Of Random Variables

scholarly journals On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 727 ◽  
Author(s):  
Dongming Nie ◽  
Saima Rashid ◽  
Ahmet Ocak Akdemir ◽  
Dumitru Baleanu ◽  
Jia-Bao Liu
Keyword(s):  
Numerical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Random Variables ◽  
Higher Moments ◽  
Weighted Inequalities ◽  
Convex Mapping ◽  
Error Estimations ◽  
Moments Of Random Variables

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

scholarly journals The space $D$ in several variables: random variables and higher moments

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Random Variables ◽  
Higher Moments ◽  
Multilinear Form ◽  
Standard Case ◽  
Random Functions ◽  
Several Variables ◽  
Random Elements ◽  
Point Evaluations

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $\sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.

A Note on the Moments of Random Variables

2007 ◽  
Vol 22 (2) ◽  
Author(s):  
Surath Sen ◽  
Elart von Collani
Keyword(s):  
Random Variables ◽  
Moments Of Random Variables

scholarly journals New-type Hoeffding’s inequalities and application in tail bounds

2021 ◽  
Vol 5 (1) ◽  
pp. 248-261
Author(s):  
Pingyi Fan ◽  
Keyword(s):  
Information Processing ◽  
Random Variables ◽  
Order Moment ◽  
First Order ◽  
Hoeffding’S Inequalities ◽  
New Type ◽  
Hoeffding’S Inequality ◽  
Hoeffding Inequality ◽  
Moments Of Random Variables ◽  
Refined Version

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz [<a href="#1">1</a>]. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refined version by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.

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