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Introduction to Random Chaos



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ISBN 9780412050916
Published March 26, 1998 by Chapman and Hall/CRC
304 Pages

 
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Book Description

Introduction to Random Chaos contains a wealth of information on this significant area, rooted in hypercontraction and harmonic analysis. Random chaos statistics extend the classical concept of empirical mean and variance. By focusing on the three models of Rademacher, Poisson, and Wiener chaos, this book shows how an iteration of a simple random principle leads to a nonlinear probability model- unifying seemingly separate types of chaos into a network of theorems, procedures, and applications.

The concepts and techniques connect diverse areas of probability, algebra, and analysis and enhance numerous links between many fields of science.

Introduction to Random Chaos serves researchers and graduate students in probability, analysis, statistics, physics, and applicable areas of science and technology.

Table of Contents

Preliminaries
Chaos Iteration
Martingales
Discrete Time Homogeneous Chaos
Random Measure and Integral
Jump Processes
Wiener Chaos
Rademacher Chaos
Martingale Chaos
More Hypercontraction
Poisson Integration: Aftermath
Transformations
Variation of Monotone Functions
Some Probability in F-Spaces
Stable and Pareto Variables

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Reviews

"[T]he book is a good mathematical treatise on Rademacher, Poisson, and Wiener stochastic processes and adequate random, or stochastic measures."
- Zentralblatt MATH, 1053