Stochastic Inequalities and Applications

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 Lévy 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 Reduction in Extremal Problems for Moments of Linear Combinations of Vectors with Random Coefficients.- III. Empirical Processes.- Moderate Deviations of Empirical Processes.- Concentration Inequalities for Sub-Additive Functions Using the Entropy Method.- Ratio Limit Theorems for Empirical Processes.- Asymptotic Distributions of Trimmed Wasserstein Distances Between the True and the Empirical Distribution Functions.- IV. Stochastic Differential Equations.- On the Rate of Convergence of Splitting-up Approximations for SPDEs.- Lower Bounds for Densities of Uniformly Elliptic Non-homogeneous Diffusions.- Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps.- Stochastic Differential Equations with Additive Fractional Noise and Locally Unbounded Drift.