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概率不等式（英文版）


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概率不等式（英文版）
  • 书号：9787030255624
    作者：林正炎
  • 外文书名：
  • 装帧：平装
    开本：特16
  • 页数：196
    字数：300
    语种：
  • 出版社：科学出版社
    出版时间：2015/6/18
  • 所属分类：概率论/数理统计
  • 定价： ￥48.00元
    售价： ￥37.92元
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本书尽可能完整地收集整理概率统计中的常用不等式，包括有关事件的概率的初等不等式，关于常用分布的不等式，关于特征函数的不等式，两个分布函数的差的估计，随机变量的概率不等式，用矩估计概率的界，概率的指数型估计，关于一个或两个随机变量的矩不等式，随机变量和的（极大的）矩估计，关于相依随机变量的不等式，关于随机过程和取值于Banach空间的随机变量的不等式等。
本书尽可能完整地收集整理概率统计中的常用不等式，包括有关事件的概率的初等不等式，关于常用分布的不等式，关于特征函数的不等式，两个分布函数的差的估计，随机变量的概率不等式，用矩估计概率的界，概率的指数型估计，关于一个或两个随机变量的矩不等式，随机变量和的（极大的）矩估计，关于相依随机变量的不等式，关于随机过程和取值于Banach空间的随机变量的不等式等。
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目录

  • 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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