LEADER 04628nam 2200625Ia 450 001 9910811501603321 005 20240313121715.0 010 $a1-283-90006-8 010 $a981-4412-58-9 035 $a(CKB)3280000000002160 035 $a(EBL)1109709 035 $a(OCoLC)826853977 035 $a(SSID)ssj0000914633 035 $a(PQKBManifestationID)11570769 035 $a(PQKBTitleCode)TC0000914633 035 $a(PQKBWorkID)10863543 035 $a(PQKB)11595610 035 $a(MiAaPQ)EBC1109709 035 $a(WSP)00002856 035 $a(Au-PeEL)EBL1109709 035 $a(CaPaEBR)ebr10640622 035 $a(CaONFJC)MIL421256 035 $a(EXLCZ)993280000000002160 100 $a20111102d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInequalities in analysis and probability /$fOdile Pons 205 $a1st ed. 210 $aSingapore $cWorld Scientific$d2013 215 $a1 online resource (232 p.) 300 $aDescription based upon print version of record. 311 $a981-4412-57-0 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Cauchy and Holder inequalities; 1.3 Inequalities for transformed series and functions; 1.4 Applications in probability; 1.5 Hardy's inequality; 1.6 Inequalities for discrete martingales; 1.7 Martingales indexed by continuous parameters; 1.8 Large deviations and exponential inequalities; 1.9 Functional inequalities; 1.10 Content of the book; 2. Inequalities for Means and Integrals; 2.1 Introduction; 2.2 Inequalities for means in real vector spaces; 2.3 Holder and Hilbert inequalities; 2.4 Generalizations of Hardy's inequality 327 $a2.5 Carleman's inequality and generalizations2.6 Minkowski's inequality and generalizations; 2.7 Inequalities for the Laplace transform; 2.8 Inequalities for multivariate functions; 3. Analytic Inequalities; 3.1 Introduction; 3.2 Bounds for series; 3.3 Cauchy's inequalities and convex mappings; 3.4 Inequalities for the mode and the median; 3.5 Mean residual time; 3.6 Functional equations; 3.7 Carlson's inequality; 3.8 Functional means; 3.9 Young's inequalities; 3.10 Entropy and information; 4. Inequalities for Martingales; 4.1 Introduction 327 $a4.2 Inequalities for sums of independent random variables4.3 Inequalities for discrete martingales; 4.4 Inequalities for martingales indexed by R+; 4.5 Poisson processes; 4.6 Brownian motion; 4.7 Diffusion processes; 4.8 Level crossing probabilities; 4.9 Martingales in the plane; 5. Functional Inequalities; 5.1 Introduction; 5.2 Exponential inequalities for functional empirical processes; 5.3 Exponential inequalities for functional martingales; 5.4 Weak convergence of functional processes; 5.5 Differentiable functionals of empirical processes; 5.6 Regression functions and biased length 327 $a5.7 Regression functions for processes6. Inequalities for Processes; 6.1 Introduction; 6.2 Stationary processes; 6.3 Ruin models; 6.4 Comparison of models; 6.5 Moments of the processes at Ta; 6.6 Empirical process in mixture distributions; 6.7 Integral inequalities in the plane; 6.8 Spatial point processes; 7. Inequalities in Complex Spaces; 7.1 Introduction; 7.2 Polynomials; 7.3 Fourier and Hermite transforms; 7.4 Inequalities for the transforms; 7.5 Inequalities in C; 7.6 Complex spaces of higher dimensions; 7.7 Stochastic integrals; Appendix A Probability 327 $aA.1 Definitions and convergences in probability spacesA.2 Boundary-crossing probabilities; A.3 Distances between probabilities; A.4 Expansions in L2(R); Hermite polynomials; Bibliography; Index 330 $aThe book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail. 606 $aFunctional analysis 606 $aProbabilities 615 0$aFunctional analysis. 615 0$aProbabilities. 676 $a515.26 700 $aPons$b Odile$01090182 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811501603321 996 $aInequalities in analysis and probability$92608170 997 $aUNINA