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 xii, 416 p. ; 26 cm.
 Notes
 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 fdivergence  7. Approximation via representations of Csiszar's fdivergence  8. Sharp high degree estimation of Csiszar's fdivergence  9. Csiszar's fdivergence as a measure of dependence 10. Optimal estimation of discrete Csiszar fdivergence  11. About a general discrete measure of dependence  12. HölderLike Csiszar's fdivergence inequalities  13. Csiszar's discrimination and Ostrowski inequalities via Eulertype and Fink identities  14. TaylorWidder representations and Grüss, Means, Ostrowski and Csiszar's inequalities  15. Representations of functions and Csiszar's fdivergence  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. ChebyshevGrüss 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.Includes bibliographical references and index.Summary: "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 discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is selfcontained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end. The topics covered in this unique book are wideranging and diverse. The opening chapters examine the probabilistic Ostrowski type inequalities, and various related ones, as well as the largely discusses about the Grothendieck type probabilistic inequalities. The book is also about inequalities in information theory and the Csiszar's fDivergence between probability measures. A great section of the book is also devoted to the applications in various directions of Geometry Moment Theory. Also, the development of the Grüss type and ChebyshevGrüss type inequalities for Stieltjes integrals and the applications in probability are explored in detail. The final chapters discuss the important real analysis methods with potential applications to stochastics. The book will be of interest to researchers and graduate students, and it is also seen as an invaluable reference book to be acquired by all science libraries as well as seminars that conduct discussions on related topics."  Publisher's website.