Stochastic Inequalities and Applications

Front Matter....Pages i-viii
Front Matter....Pages 1-1
Large Deviations of Typical Linear Functionals on a Convex Body with Unconditional Basis....Pages 3-13
A Concentration Inequality on Riemannian Path Space....Pages 15-21
A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration....Pages 23-32
Concentration Inequalities for Convex Functions on Product Spaces....Pages 33-52
Front Matter....Pages 53-53
Exponential Inequalities, with Constants, for U-statistics of Order Two....Pages 55-69
On a.s. Unconditional Convergence of Random Series in Banach Spaces....Pages 71-75
Moment and Tail Estimates for Multidimensional Chaos Generated by Positive Random Variables with Logarithmically Concave Tails....Pages 77-92
A Quantitative Law of Large Numbers via Exponential Martingales....Pages 93-111
Sufficient Conditions for Boundedness of Moving Average Processes....Pages 113-128
Notes on the Speed of Entropic Convergence in the Central Limit Theorem....Pages 129-156
On a Nonsymmetric Version of the Khinchine-Kahane Inequality....Pages 157-168
Dimensionality Reduction in Extremal Problems for Moments of Linear Combinations of Vectors with Random Coefficients....Pages 169-185
Front Matter....Pages 187-187
Moderate Deviations of Empirical Processes....Pages 189-212
Concentration Inequalities for Sub-Additive Functions Using the Entropy Method....Pages 213-247
Ratio Limit Theorems for Empirical Processes....Pages 249-278
Asymptotic Distributions of Trimmed Wasserstein Distances Between the True and the Empirical Distribution Function....Pages 279-298
Front Matter....Pages 299-299
On the Rate of Convergence of Splitting-up Approximations for SPDEs....Pages 301-321
Lower Bounds for Densities of Uniformly Elliptic Non-homogeneous Diffusions....Pages 323-338
Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps....Pages 339-351
Stochastic Differential Equations with Additive Fractional Noise and Locally Unbounded Drift....Pages 353-365
Back Matter....Pages 367-367