Modern Theory of Summation of Random Variables

Vladimir M. Zolotarev

• Publisher: De Gruyter
• Year: 2011
• Print ISBN: 9783110631241
• eBook ISBN: 9783110936537
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

No detailed description available for "Modern Theory of Summation of Random Variables".

Table of contents

• Foreword
• Preface
• 1 Introduction to the theory of probability metrics
• 1.1 Probability metrics
• 1.2 Minimal and protominimal metrics
• 1.3 Special minimal and protominimal metrics
• 1.4 Ideal metrics
• 1.5 Relationships between metrics
• 1.6 Linearly invariant metrics
• 2 The nature of limit theorems
• 2.1 The history of limit theorems
• 2.2 A generalization of the Lindeberg-Feller theorem
• 2.3 Natural estimates of convergence rate in the central limit theorem
• 2.4 Limit theorems as stability theorems
• 2.5 One more mechanism forming the central limit theorem
• 3 The normalization of random sequences
• 3.1 General normalization problems
• 3.2 The choice of constants under linear normalization
• 4 Centers and scatters of random variables
• 4.1 The definition and properties of index, centers and scatters
• 4.2 An analog of the Chebyshev inequality
• 4.3 Centers and scatters in the criteria of L-compactness
• 4.4 Centers and scatters in the criteria of L-convergence of random sequences
• 5 Classical theory of limit theorems for sums of independent random variables
• 5.1 Reduced models
• 5.2 Infinitely divisible laws
• 5.3 Limit theorems of the classical theory
• 5.4 The estimates of accuracy of approximations in limit theorems of the classical theory
• 5.5 On completeness of classical theory
• 6 Generalizations of the classical theory of summation of independent random variables
• 6.1 The history of the problem
• 6.2 Stability of compositions of distributions
• 6.3 Limit theorems in a non-classical setting
• 6.4 Limit theorems in the generalized summation scheme
• 6.5 The method of metric distances
• 6.6 Sums of non-independent random variables
• Bibliography
• Index