LEADER 04602nam a2200325 i 4500 001 991000512199707536 008 100112s2010 si b 001 0 eng d 020 $a9789814280785 020 $a981428078X 035 $ab13868354-39ule_inst 040 $aDip.to Matematica$beng 082 04$a519.2$222 084 $aAMS 60E15 084 $aLC QA274.A64 100 1 $aAnastassiou, George A.$060024 245 10$aProbabilistic inequalities /$cGeorge A. Anastassiou 260 $aSingapore ;$aHackensack, NJ ;$aLondon :$bWorld Scientific,$cc2010 300 $axii, 416 p. ;$c26 cm 440 0$aSeries on concrete and applicable mathematics ;$v7 504 $aIncludes bibliographical references and index 505 0 $a1. 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. Hčolder-Like Csiszar's f-divergence inequalities ; 13. Csiszar's discrimination and Ostrowski inequalities via Euler-type and Fink identities ; 14. Taylor-Widder representations and Grčuss, 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. Grčuss type inequalities using the Stieltjes integral ; 26. Chebyshev-Grčuss 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 520 1 $a"In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end. The topics covered in this unique book are wide-ranging and diverse. The opening chapters examine the probabilistic Ostrowski type inequalities, and various related ones, as well as the largely discusses about the Grothendieck type probabilistic inequalities. The book is also about inequalities in information theory and the Csiszar's f-Divergence between probability measures. A great section of the book is also devoted to the applications in various directions of Geometry Moment Theory. Also, the development of the Grčuss type and Chebyshev-Grčuss type inequalities for Stieltjes integrals and the applications in probability are explored in detail. The final chapters discuss the important real analysis methods with potential applications to stochastics. The book will be of interest to researchers and graduate students, and it is also seen as an invaluable reference book to be acquired by all science libraries as well as seminars that conduct discussions on related topics.": P.[4] of cover 650 0$aProbabilities 650 0$aInequalities (Mathematics) 907 $a.b13868354$b02-04-14$c12-01-10 912 $a991000512199707536 945 $aLE013 60E ANA12 (2010)$g1$i2013000211800$lle013$op$pE84.60$q-$rl$s- $t0$u2$v0$w2$x0$y.i15080596$z22-02-10 996 $aProbabilistic inequalities$9230075 997 $aUNISALENTO 998 $ale013$b12-01-10$cm$da $e-$feng$gsi $h0$i0