Ebook: Stochastic Inequalities and Applications

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.

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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.

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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.

Content:
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

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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.

Content:
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
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