Inequalities in Analysis and Probability
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Book Overview Preface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Cauchy and Holder inequalities; 1.3 Inequalities for transformed series and fu...
Preface; 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. - 2.5 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. - 4.2 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.
Book Details Format: Hardcover | Pages: 221 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9814412570
FormatHardcover
Pages221
LanguageEnglish
ISBN9814412570
EAN9789814412575
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date1970-01-01
Edition1
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.2 Pounds
Length9.0 Inches
Width6.0 Inches
Height0.8 Inches
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