Stochastic Inequalities and Applications [Paperback]

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.

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.

I. Geometric Inequalities.- Large Deviations of Typical Linear Functionals on a Convex Body with Unconditional Basis.- A Concentration Inequality on Riemannian Path Space.- A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration.- Concentration Inequalities for Convex Functions on Product Spaces.- II. Independent Random Vectors, Chaos, Martingales and L?vy Processes.- Exponential Inequalities, with Constants, for U-statistics of Order Two.- On a.s. Unconditional Convergence of Random Series in Banach Spaces.- Moment and Tail Estimates for Multidimensional Chaoses Generated by Positive Random Variables with Logarithmically Concave Tails.- A Quantitative Law of Large Numbers via Exponential Martingales.- Sufficient Conditions for Boundedness of Moving Average Processes.- Notes on the Speed of Entropic Convergence in the Central Limit Theorem.- On a Nonsymmetric Version of the Khinchine-Kahane Inequality.- Dimensionality Reductiol£.