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Field name	Details
Dewey Class	519
Title	Sums of Independent Random Variables ([EBook] /) / by Valentin V. Petrov.
Author	Petrov, Valentin V.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg, , 1975.
Physical Details	X, 348 p. : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete 0071-1136 ; ; 82
ISBN	9783642658099
Contents note	I. Probability Distributions and Characteristic Functions -- § 1. Random variables and probability distributions -- § 2. Characteristic functions -- § 3. Inversion formulae -- § 4. The convergence of sequences of distributions and characteristic functions -- § 5. Supplement -- II. Infinitely Divisible Distributions -- § 1. Definition and elementary properties of infinitely divisible distributions -- § 2. Canonical representation of infinitely divisible characteristic functions -- § 3. An auxiliary theorem -- § 4. Supplement -- III. Some Inequalities for the Distribution of Sums of Independent Random Variables -- § 1. Concentration functions -- § 2. Inequalities for the concentration functions of sums of independent random variables -- § 3. Inequalities for the distribution of the maximum of sums of independent random variables -- § 4. Exponential estimates for the distributions of sums of independent random variables -- § 5. Supplement -- IV. Theorems on Convergence to Infinitely Divisible Distributions -- § 1. Infinitely divisible distributions as limits of the distributions of sums of independent random variables -- § 2. Conditions for convergence to a given infinitely divisible distribution -- § 3. Limit distributions of class L and stable distributions -- § 4. The central limit theorem -- § 5. Supplement -- V. Estimates of the Distance Between the Distribution of a Sum of Independent Random Variables and the Normal Distribution -- § 1. Estimating the nearness of functions of bounded variation by the nearness of their Fourier-Stieltjes transforms -- § 2. The Esseen and Berry-Esseen inequalities -- § 3. Generalizations of Esseen’s inequality -- § 4. Non-uniform estimates -- § 5. Supplement -- VI. Asymptotic Expansions in the Central Limit Theorem -- § 1. Formal construction of the expansions -- § 2 Auxiliary propositions -- § 3. Asymptotic expansions of the distribution function of a sum of independent identically distributed random variables -- § 4. Asymptotic expansions of the distribution function of a sum of independent non-identically distributed random variables, and of the derivatives of this function -- § 5. Supplement -- VII. Local Limit Theorems -- § 1. Local limit theorems for lattice distributions -- § 2. Local limit theorems for densities -- § 3. Asymptotic expansions in local limit theorems -- § 4. Supplement -- VIII. Probabilities of Large Deviations -- § 1. Introduction -- § 2. Asymptotic relations connected with Cramér’s series -- § 3. Necessary and sufficient conditions for normal convergence in power zones -- § 4. Supplement -- IX. Laws of Large Numbers -- § 1. The weak law of large numbers -- § 2. Convergence of series of independent random variables -- § 3. The strong law of large numbers -- § 4. Convergence rates in the laws of large numbers -- § 5. Supplement -- X. The Law of the Iterated Logarithm -- § 1. Kolmogorov’s theorem -- § 2. Generalization of Kolmogorov’s theorem -- § 3. The central limit theorem and the law of the iterated logarithm -- § 4. Supplement -- Notes on Sources in the Literature -- References -- Subject Indes -- Table of Symbols and Abbreviations.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-65809-9
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Engineering mathematics . Mathematics . Authors: Petrov, Valentin V. . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete . Classification: 519 .

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Sums of Independent Random Variables

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