Random Variables and Probability Distributions

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Cambridge University Press, Jun 3, 2004 - Mathematics - 132 pages
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.
 

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Contents

Axioms and preliminary theorems
9
SECOND PART DISTRIBUTIONS IN
18
Characteristic functions
24
Addition of independent variables Conver
36
The normal distribution and the central limit
50
Error estimation Asymptotic expansions
70
A class of stochastic processes
89
THIRD PART DISTRIBUTIONS IN
100
The normal distribution and the central limit
109
Bibliography
115
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