Probabilistic inequalities
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Hackensack, N.J. :
World Scientific,
c2010.
|
| Edice: | Series on concrete and applicable mathematics ;
v. 7. |
| Témata: | |
| On-line přístup: | An electronic book accessible through the World Wide Web; click to view |
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Obsah:
- 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.