Characterization of distributions by the method of intensively monotone operators / Ashot V. Kakosyan, Leo B. Klebanov, Joseph A. Melamed

Auteur: Kakosian, Ashot Vazrikievich (1948-) - AuteurCo-auteur: Klebanov, Lev Borisovich (1946-) - Auteur ; Melamed, Iosif Aleksandrovich (1948-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1088Langue: anglaisÉditeur: Berlin : Springer-Verlag, 1984 ISBN: 9783540390503 Note: The problem of solving characterization problems often can be reduced to that of proving the uniqueness of solutions of functional equations. The present work deals with functional equations which can be written as operator equations, where the operators involved are intensively monotone. The authors pose a large number of various characterization problems associated with operator equations of this type. These problems are solved by using some results on uniqueness of positive solutions of operator equations. The titles of the five chapters are as follows: 1. Intensively monotone operators and their properties; 2. Characterization problems associated with properties of linear statistics; 3. Characterization problems associated with nonlinear statistics and problems of reconstruction of distributions; 4. On some problems of characterization of distributions associated with the mathematical theory of reliability; 5. Characterizations of multivariate distributions. (MathSciNet) Sujets MSC: 62E10 Statistics -- Distribution theory -- Characterization and structure theory
47H05 Operator theory -- Nonlinear operators and their properties -- Monotone operators and generalizations
62H05 Statistics -- Multivariate analysis -- Characterization and structure theory
47H10 Operator theory -- Nonlinear operators and their properties -- Fixed-point theorems
47J05 Operator theory -- Equations and inequalities involving nonlinear operators -- Equations involving nonlinear operators (general)
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The problem of solving characterization problems often can be reduced to that of proving the uniqueness of solutions of functional equations. The present work deals with functional equations which can be written as operator equations, where the operators involved are intensively monotone. The authors pose a large number of various characterization problems associated with operator equations of this type. These problems are solved by using some results on uniqueness of positive solutions of operator equations.
The titles of the five chapters are as follows: 1. Intensively monotone operators and their properties; 2. Characterization problems associated with properties of linear statistics; 3. Characterization problems associated with nonlinear statistics and problems of reconstruction of distributions; 4. On some problems of characterization of distributions associated with the mathematical theory of reliability; 5. Characterizations of multivariate distributions. (MathSciNet)

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