Stochastic Inequalities and Applications
Author: Evarist Giné
Format: Unknown Binding
Release Date: April 29, 2004
Concentration inequalities, which express the fact that certain complicated random variables are almost constant on almost the whole space, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to entropy, transportation costs and geometry, along with applications in hypothesis testing and information theory, multilinear forms and U-statistics, Rademacher processes, moderate and large deviations, empirical processes and regression, Markov processes and queuing theory. Extensions of classical and basic moment inequalities to linear and multilinear forms in independent random variables and vectors, and new results on the rate of convergence in the central limit theorem, can be found here as well. The book also contains a sample of recent advances on several aspects of stochastic analysis such as diffusion processes, stochastic differential equations driven by fractional Brownian motion, Lyapunov exponents for stochastic differential equations with jumps, and Levy processes.