Schur lemma and limit theorems in lattice groups with respect to filters

2012 ◽  
Vol 62 (6) ◽  
Author(s):  
A. Boccuto ◽  
X. Dimitriou ◽  
N. Papanastassiou
Keyword(s):  
Open Problem ◽  
Limit Theorems ◽  
Filter Convergence ◽  
Schur Lemma

AbstractSome Schur, Nikodým, Brooks-Jewett and Vitali-Hahn-Saks-type theorems for (ℓ)-group-valued measures are proved in the setting of filter convergence. Finally we pose an open problem.

scholarly journals Open Problem—Iterative Schemes for Stochastic Optimization: Convergence Statements and Limit Theorems

2019 ◽  
Vol 9 (3) ◽  
pp. 299-302 ◽  
Author(s):  
Afrooz Jalilzadeh ◽  
Jinlong Lei ◽  
Uday V. Shanbhag
Keyword(s):  
Stochastic Optimization ◽  
Open Problem ◽  
Limit Theorems ◽  
Iterative Schemes

scholarly journals Limit Theorems for k-Subadditive Lattice Group-Valued Capacities in The Filter Convergence Setting

2016 ◽  
Vol 65 (1) ◽  
pp. 1-21
Author(s):  
Antonio Boccuto ◽  
Xenofon Dimitriou
Keyword(s):  
Limit Theorems ◽  
Open Problems ◽  
Lattice Group ◽  
Set Functions ◽  
Filter Convergence

Abstract We investigate some properties of lattice group-valued positive, monotone and k-subadditive set functions, and in particular, we give some comparisons between regularity and continuity from above. Moreover, we prove different kinds of limit theorems with respect to filter convergence. Furthermore, some open problems are posed.

scholarly journals Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Antonio Boccuto ◽  
Xenofon Dimitriou
Keyword(s):  
Limit Theorems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Open Problems ◽  
Set Functions ◽  
Filter Convergence ◽  
Abstract Structure ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for exchange of limits of double-indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence. As a consequence, we give some filter limit theorems and some characterization of continuity and semicontinuity of the limit of a pointwise convergent family of set functions. Furthermore, we pose some open problems.

Limit theorems and price changes in financial markets

1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Limit Theorems ◽  
Price Changes

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

Limit theorems for long-memory flows on Wiener chaos

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1473-1503 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Memory ◽  
Limit Theorems ◽  
Wiener Chaos

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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