Random variables and probability distributions
著者
書誌事項
Random variables and probability distributions
（Cambridge tracts in mathematics and mathematical physics, no. 36）
Cambridge University Press, 2004
3rd ed, paperback ed.
- : pbk
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注記
Bibliography: p. [115]-118
内容説明・目次
内容説明
This tract develops the purely mathematical side of the theory of probability, without reference to any applications. When originally published, it was one of the earliest works in the field built on the axiomatic foundations introduced by A. Kolmogoroff in his book Grundbegriffe der Wahrscheinlichkeitsrechnung, thus treating the subject as a branch of the theory of completely additive set functions. The author restricts himself to a consideration of probability distributions in spaces of a finite number of dimensions, and to problems connected with the Central Limit Theorem and some of its generalizations and modifications. In this edition the chapter on Liapounoff's theorem has been partly rewritten, and now includes a proof of the important inequality due to Berry and Esseen. The terminology has been modernized, and several minor changes have been made.
目次
- Preface to the first edition
- Preface to the second edition
- Preface to the third edition
- Abbreviations
- Part I. Principles: 1. Introductory remarks
- 2. Axioms and preliminary theorems
- Part II. Distributions in R1: 3. General properties
- 4. Characteristic functions
- 5. Addition of independent variables
- 6. The normal distribution and the central limit theorem
- 7. Error estimation
- 8. A class of stochastic processes
- Part III. Distributions in R2: 9. General properties
- 10. The normal distribution and the central limit theorem
- Bibliography.
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