Chapter 1 Elementary Inequalities of Probabilities of Events 1.1 Inclusion-exclusion Formula 1.2 Corollaries of the Inclusion-exclusion Formula 1.3 Further Consequences of the Inclusion-exclusion Formula 1.4 Inequalities Related to Symmetric Difference 1.5 Inequalities Related to Independent Events 1.6 Lower Bound for Union (Chung-Erdos) References Chapter 2 Inequalities Related to Commonly Used Distributions 2.1 Inequalities Related to the Normal d.f. 2.2 Slepian Type Inequalities 2.3 Anderson Type Inequalities 2.4 Khatri-Sidak Type Inequalities 2.5 Corner Probability of Normal Vector 2.6 Normal Approximations of Binomial and Poisson Distributions References Chapter 3 Inequalities Related to Characteristic Functions 3.1 Inequalities Related Only with c.f. 3.2 Inequalities Related to c.f.and d.f. 3.3 Normality Approximations of c.f.of Independent Sums References Chapter 4 Estimates of the Difference of Two Distribution Functions 4.1 Fourier Transformation 4.2 Stein-Chen Method 4.3 Stieltjes Transformation References Chapter 5 Probability Inequalities of Random Variables 5.1 Inequalities Related to Two r.v.'s 5.2 Perturbation Inequality 5.3 Symmetrization Inequalities 5.4 Levy Inequality 5.5 Bickel Inequality 5.6 Upper Bounds of Tail Probabilities of Partial Sums 5.7 Lower Bounds of Tail Probabilities of Partial Sums 5.8 Tail Probabilities for Maximum Partial Sums 5.9 Tail Probabilities for Maximum Partial Sums (Continuation) 5.10 Reflection Inequality of Tail Probability (HoffmannJorgensen) 5.11 Probability of Maximal Increment (Shao) 5.12 Mogulskii Minimal Inequality 5.13 Wilks Inequality References Chapter 6 Bounds of Probabilities in Terms of Moments 6.1 Chebyshev-Markov Type Inequalities 6.2 Lower Bounds 6.3 Series of Tail Probabilities 6.4 Kolmogorov Type Inequalities 6.5 Generalization of Kolmogorov Inequality for a Submartingale 6.6 Renyi-Hajek Type Inequalities 6.7 Chernoff Inequality 6.8 Fuk and Nagaev Inequality 6.9 Burkholder Inequality 6.10 Complete Convergence of Partial Sums References Chapter 7 Exponential Type Estimates of Probabilities 7.1 Equivalence of Exponential Estimates 7.2 Petrov Exponential Inequalities 7.3 Hoeffding Inequality 7.4 Bennett Inequality 7.5 Bernstein Inequality 7.6 Exponential Bounds for Sums of Bounded Variables 7.7 Kolmogorov Inequalities 7.8 Prokhorov Inequality 7.9 Exponential Inequalities by Censoring 7.10 Tail Probability of Weighted Sums References Chapter 8 Moment Inequalities Related to One or Two Variables 8.1 Moments of Truncation 8.2 Exponential Moment of Bounded Variables 8.3 Holder Type Inequalities 8.4 Jensen Type Inequalities 8.5 Dispersion Inequality of Censored Variables 8.6 Monotonicity of Moments of Sums 8.7 Symmetrization Moment Inequatilies 8.8 Kimball Inequality 8.9 Exponential Moment of Normal Variable 8.10 Inequatilies of Nonnegative Variable 8.11 Freedman Inequality 8.12 Exponential Moment of Upper Truncated Variables References Chapter 9 Moment Estimates of (Maximum of) Sums of Random Variables 9.1 Elementary Inequalities 9.2 Minkowski Type Inequalities 9.3 The Case 1≤r≤2 9.4 The Case r≥2 9.5 Jack-knifed Variance 9.6 Khintchine Inequality 9.7 Marcinkiewicz-Zygmund-Burkholder Type Inequalities 9.8 Skorokhod Inequalities 9.9 Moments of Weighted Sums 9.10 Doob Crossing Inequalities 9.11 Moments of Maximal Partial Sums 9.12 Doob Inequalities 9.13 Equivalence Conditions for Moments 9.14 Serfling Inequalities 9.15 Average Fill Rate References Chapter 10 Inequalities Related to Mixing Sequences 10.1 Covariance Estimates for Mixing Sequences 10.2 Tail Probability on a-mixing Sequence 10.3 Estimates of 4-th Moment on p-mixing Sequence 10.4 Estimates of Variances of Increments of p-mixing Sequence 10.5 Bounds of 2+o-th Moments of Increments of p-mixing Sequence 10.6 Tail Probability on e-mixing Sequence 10.7 Bounds of 2+o-th Moment of Increments of e-mixing Sequence 10.8 Exponential Estimates of Probability on e-mixing Sequence References Chapter 11 Inequalities Related to Associative Variables 11.1 Covariance of PQD Varaibles 11.2 Probability of Quadrant on PA (NA) Sequence 11.3 Estimates of c.f.'s on LPQD (LNQD) Sequence 11.4 Maximal Partial Sums of PA Sequence 11.5 Variance of Increment of LPQD Sequence 11.6 Expectation of Convex Function of Sum of NA Sequence 11.7 Marcinkiewicz-Zygmund-Burkholder Inequality for NA Sequence References Chapter 12 Inequalities about Stochastic Processes and Banach Space Valued Random Variables 12.1 Probability Estimates of Supremums of a Wiener Process 12.2 Probability Estimate of Supremum of a Poisson Process 12.3 Fernique Inequality 12.4 Borell Inequality 12.5 Tail Probability of Gaussian Process 12.6 Tail Probability of Randomly Signed Independent Processes 12.7 Tail Probability of Adaptive Process 12.8 Tail Probability on Submartingale 12.9 Tail Probability of Independent Sum in B-Space 12.10 Isoperimetric Inequalities 12.11 Ehrhard Inequality 12.12 Tail Probability of Normal Variable in B-Space 12.13 Gaussian Measure on Symmetric Convex Sets 12.14 Equivalence of Moments of B-Gaussian Variables 12.15 Contraction Principle 12.16 Symmetrization Inequalities in B-Space 12.17 Decoupling Inequality References
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