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## Details

Genre/Form: | Electronic books |
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Additional Physical Format: | Print version: Anastassiou, George A., 1952- Probabilistic inequalities. Hackensack, NJ : World Scientific, ©2010 (DLC) 2010285064 (OCoLC)644019708 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
George A Anastassiou |

ISBN: | 9789814280792 9814280798 |

OCLC Number: | 671654956 |

Description: | 1 online resource (xii, 416 pages). |

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. |

Series Title: | Series on concrete and applicable mathematics, v. 7. |

Responsibility: | George A. Anastassiou. |

### Abstract:

Presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. This book deals with inequalities in information theory and the Csiszar's f-Divergence between probability measures.
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Publisher Synopsis

The book is a useful source for references to many results which are not covered by numerous books well-known in Probability Theory. The book under consideration is addressed to the researchers and graduate students. It could be employed to prepare special courses and also to discuss the material at the research seminars. -- Zentralblatt MATH "Zentralblatt MATH" Read more...

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