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 ar...
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| Main Author: | |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, N.J. :
World Scientific,
c2010.
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| Series: | Series on concrete and applicable mathematics ;
v. 7. |
| Subjects: | |
| Online Access: | An electronic book accessible through the World Wide Web; click to view |
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Table of Contents:
- 1. Introduction
- 2. Basic stochastic Ostrowski inequalities
- 3. Multidimensional Montgomery identities and Ostrowski type inequalities
- 4. General probabilistic inequalities
- 5. About Grothendieck inequalities
- 6. Basic optimal estimation of Csiszar's f-divergence
- 7. Approximation via representations of Csiszar's f-divergence
- 8. Sharp high degree estimation of Csiszar's f-divergence
- 9. Csiszar's f-divergence as a measure of dependence
- 10. Optimal estimation of discrete Csiszar f-divergence
- 11. About a general discrete measure of dependence
- 12. Hölder-Like Csiszar's f-divergence inequalities
- 13. Csiszar's discrimination and Ostrowski inequalities via Euler-type and Fink identities
- 14. Taylor-Widder representations and Grüss, Means, Ostrowski and Csiszar's inequalities
- 15. Representations of functions and Csiszar's f-divergence
- 16. About general moment theory
- 17. Extreme bounds on the average of a rounded off observation under a moment condition
- 18. Moment theory of random rounding rules subject to one moment condition
- 19. Moment theory on random rounding rules using two moment conditions
- 20. Prokhorov radius around zero using three moment constraints
- 21. Precise rates of Prokhorov convergence using three moment conditions
- 22. On Prokhorov convergence or probability measures to the unit under three moments
- 23. Geometric moment methods applied to optimal portfolio
- 24. Discrepancies between general integral means
- 25. Grüss type inequalities using the Stieltjes integral
- 26. Chebyshev-Grüss type and difference of integral means inequalities using the Stieltjes integral
- 27. An expansion formula
- 28. Integration by parts on the multidimensional domain
- Bibliography
- List of symbols.