Probabilistic Inequalities.

In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: World Scientific 2009.
Temas:
Probabilities.
Inequalities (Mathematics)
Probability
Probabilités.
Inégalités (Mathématiques)
probability.
Probabilities
Electronic resource.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover13;
  • Contents
  • Preface
  • 1. Introduction
  • 2. Basic Stochastic Ostrowski Inequalities
  • 2.1 Introduction
  • 2.2 One Dimensional Results
  • 2.3 Multidimensional Results
  • 2.4 Applications
  • 2.5 Addendum
  • 3. Multidimensional Montgomery Identities and Ostrowski type Inequalities
  • 3.1 Introduction
  • 3.2 Results
  • 3.3 Application to Probability Theory
  • 4. General Probabilistic Inequalities
  • 4.1 Introduction
  • 4.2 Make Applications
  • 4.3 Remarks on an Inequality
  • 4.4 Lq; q> 1, Related Theory
  • 5. About Grothendieck Inequalities
  • 5.1 Introduction
  • 5.2 Main Results
  • 6. Basic Optimal Estimation of Csiszar's f-Divergence
  • 6.1 Background
  • 6.2 Main Results
  • 7. Approximations via Representations of Csiszar's f-Divergence
  • 7.1 Background
  • 7.2 All Results
  • 8. Sharp High Degree Estimation of Csiszar's f-Divergence
  • 8.1 Background
  • 8.2 Results Based on Taylor's Formula
  • 8.3 Results Based on Generalized Taylor{Widder Formula
  • 8.4 Results Based on an Alternative Expansion Formula
  • 9. Csiszar's f-Divergence as a Measure of Dependence
  • 9.1 Background
  • 9.2 Results
  • 10. Optimal Estimation of Discrete Csiszar f-Divergence
  • 10.1 Background
  • 10.2 Results
  • 11. About a General Discrete Measure of Dependence
  • 11.1 Background
  • 11.2 Results
  • 12. H older-Like Csiszar's f-Divergence Inequalities
  • 12.1 Background
  • 12.2 Results
  • 13. Csiszar's Discrimination and Ostrowski Inequalities via Eulertype and Fink Identities
  • 13.1 Background
  • 13.2 Main Results
  • 14. Taylor-Widder Representations and Gr uss, Means, Ostrowski and Csiszar's Inequalities
  • 14.1 Introduction
  • 14.2 Background
  • 14.3 Main Results
  • 15. Representations of Functions and Csiszar's f-Divergence
  • 15.1 Introduction
  • 15.2 Main Results
  • 16. About General Moment Theory
  • 16.1 The Standard Moment Problem
  • 16.2 The Convex Moment Problem
  • 16.3 Infinite Many Conditions Moment Problem
  • 16.4 Applications 8211; Discussion
  • 17. Extreme Bounds on the Average of a Rounded o Observation under a Moment Condition
  • 17.1 Preliminaries
  • 17.2 Results
  • 18. Moment Theory of Random Rounding Rules Subject to One Moment Condition
  • 18.1 Preliminaries
  • 18.2 Bounds for Random Rounding Rules
  • 18.3 Comparison of Bounds for Random and Deterministic Rounding Rules
  • 19. Moment Theory on Random Rounding Rules Using Two Moment Conditions
  • 19.1 Preliminaries
  • 19.2 Results
  • 19.3 Proofs
  • 20. Prokhorov Radius Around Zero Using Three Moment Constraints
  • 20.1 Introduction and Main Result
  • 20.2 Auxiliary Moment Problem
  • 20.3 Proof of Theorem 20.1.
  • 20.4 Concluding Remarks
  • 21. Precise Rates of Prokhorov Convergence Using Three Moment Conditions
  • 21.1 Main Result
  • 21.2 Outline of Proof
  • 22. On Prokhorov Convergence of Probability Measures to the Unit under Three Moments
  • 22.1 Main Result
  • 22.2 An Auxiliary Moment Problem
  • 22.3 Further Auxiliary Results
  • 22.4 Minimizing Solutions in Boxes
  • 22.5 Conclusions
  • 23. Geometric Moment Methods Applied to Optimal Portfolio Management
  • 23.1 Introduction
  • 23.2 Preliminaries
  • 23.3 Main Results
  • 23.3.1. The Financial Portfolio Problem
  • 23.3.2. The Portfolio Problem Involving Three Securities (similarly one can trea.

Ejemplares similares