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Stochastic Inequalities and Applications : Progress in Probability - Evariste Gine

Stochastic Inequalities and Applications

Progress in Probability

By: Evariste Gine (Editor), Christian Houdre (Editor), David Nualart (Editor)

Hardcover

Published: 24th October 2003
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Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.

Prefacep. vii
Geometric Inequalities
Large Deviations of Typical Linear Functionals on a Convex Body with Unconditional Basisp. 3
A Concentration Inequality on Riemannian Path Spacep. 15
A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentrationp. 23
Concentration Inequalities for Convex Functions on Product Spacesp. 33
Independent Random Vectors, Chaos, Martingales and Levy Processes
Exponential Inequalities, with Constants, for U-statistics of Order Twop. 55
On a.s. Unconditional Convergence of Random Series in Banach Spacesp. 71
Moment and Tail Estimates for Multidimensional Chaoses Generated by Positive Random Variables with Logarithmically Concave Tailsp. 77
A Quantitative Law of Large Numbers via Exponential Martingalesp. 93
Sufficient Conditions for Boundedness of Moving Average Processesp. 113
Notes on the Speed of Entropic Convergence in the Central Limit Theoremp. 129
On a Nonsymmetric Version of the Khinchine-Kahane Inequalityp. 157
Dimensionality Reduction in Extremal Problems for Moments of Linear Combinations of Vectors with Random Coefficientsp. 169
Empirical Processes
Moderate Deviations of Empirical Processesp. 189
Concentration Inequalities for Sub-Additive Functions Using the Entropy Methodp. 213
Ratio Limit Theorems for Empirical Processesp. 249
Asymptotic Distributions of Trimmed Wasserstein Distances Between the True and the Empirical Distribution Functionsp. 279
Stochastic Differential Equations
On the Rate of Convergence of Splitting-up Approximations for SPDEsp. 301
Lower Bounds for Densities of Uniformly Elliptic Non-homogeneous Diffusionsp. 323
Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumpsp. 339
Stochastic Differential Equations with Additive Fractional Noise and Locally Unbounded Driftp. 353
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783764321970
ISBN-10: 3764321970
Series: Progress in Probability
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 367
Published: 24th October 2003
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.78