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IDENT
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http://dx.doi.org/10.1007/978-3-642-65809-9
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標題および責任表示
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Sums of Independent Random Variables / by Valentin V. Petrov
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特定資料種別コード
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リモートファイル
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出版・頒布事項
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Berlin, Heidelberg : Springer Berlin Heidelberg , 1975
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形態事項
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X, 348 p : online resource
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巻号情報
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書誌構造リンク
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Ergebnisse der Mathematik und ihrer Grenzgebiete <> 82//a
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内容著作注記
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I. Probability Distributions and Characteristic Functions
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内容著作注記
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§ 1. Random variables and probability distributions
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§ 2. Characteristic functions
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§ 3. Inversion formulae
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§ 4. The convergence of sequences of distributions and characteristic functions
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§ 5. Supplement
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内容著作注記
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II. Infinitely Divisible Distributions
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§ 1. Definition and elementary properties of infinitely divisible distributions
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§ 2. Canonical representation of infinitely divisible characteristic functions
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§ 3. An auxiliary theorem
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§ 4. Supplement
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III. Some Inequalities for the Distribution of Sums of Independent Random Variables
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§ 1. Concentration functions
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§ 2. Inequalities for the concentration functions of sums of independent random variables
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§ 3. Inequalities for the distribution of the maximum of sums of independent random variables
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§ 4. Exponential estimates for the distributions of sums of independent random variables
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§ 5. Supplement
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IV. Theorems on Convergence to Infinitely Divisible Distributions
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§ 1. Infinitely divisible distributions as limits of the distributions of sums of independent random variables
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§ 2. Conditions for convergence to a given infinitely divisible distribution
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§ 3. Limit distributions of class L and stable distributions
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§ 4. The central limit theorem
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§ 5. Supplement
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V. Estimates of the Distance Between the Distribution of a Sum of Independent Random Variables and the Normal Distribution
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§ 1. Estimating the nearness of functions of bounded variation by the nearness of their Fourier-Stieltjes transforms
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§ 2. The Esseen and Berry-Esseen inequalities
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§ 3. Generalizations of Esseen's inequality
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§ 4. Non-uniform estimates
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§ 5. Supplement
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VI. Asymptotic Expansions in the Central Limit Theorem
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§ 1. Formal construction of the expansions
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§ 2 Auxiliary propositions
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§ 3. Asymptotic expansions of the distribution function of a sum of independent identically distributed random variables
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§ 4. Asymptotic expansions of the distribution function of a sum of independent non-identically distributed random variables, and of the derivatives of this function
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§ 5. Supplement
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VII. Local Limit Theorems
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§ 1. Local limit theorems for lattice distributions
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§ 2. Local limit theorems for densities
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§ 3. Asymptotic expansions in local limit theorems
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§ 4. Supplement
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VIII. Probabilities of Large Deviations
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§ 1. Introduction
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§ 2. Asymptotic relations connected with Cramer's series
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§ 3. Necessary and sufficient conditions for normal convergence in power zones
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§ 4. Supplement
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IX. Laws of Large Numbers
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§ 1. The weak law of large numbers
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§ 2. Convergence of series of independent random variables
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§ 3. The strong law of large numbers
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§ 4. Convergence rates in the laws of large numbers
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§ 5. Supplement
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X. The Law of the Iterated Logarithm
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§ 1. Kolmogorov's theorem
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§ 2. Generalization of Kolmogorov's theorem
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§ 3. The central limit theorem and the law of the iterated logarithm
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§ 4. Supplement
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内容著作注記
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Notes on Sources in the Literature
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References
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Subject Indes
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内容著作注記
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Table of Symbols and Abbreviations
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学情ID
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9783642658112
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本文言語コード
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英語
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著者標目リンク
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*Petrov, Valentin V. <> author
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著者標目リンク
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SpringerLink (Online service) <>
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分類標目
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DC23:519
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件名標目等
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Mathematics
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件名標目等
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Applied mathematics
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件名標目等
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Engineering mathematics
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件名標目等
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Mathematics
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件名標目等
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Applications of Mathematics
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