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The Normal Distribution: Characterizations with Applications by Wlodzimierz Bryc (Paperback, 1995)

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About this product

Product Information

This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.

Product Identifiers

Publisher
Springer-Verlag New York Inc.
ISBN-13
9780387979908
eBay Product ID (ePID)
95092571

Product Key Features

Author
Wlodzimierz Bryc
Publication Name
The Normal Distribution: Characterizations with Applications
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
1995
Type
Textbook
Number of Pages
139 Pages

Dimensions

Item Height
235mm
Item Width
155mm
Volume
100
Item Weight
242g

Additional Product Features

Title_Author
Wlodzimierz Bryc
Series Title
Lecture Notes in Statistics
Country/Region of Manufacture
United States

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