1st Edition

Introduction to Random Chaos

By Jerzy Szulga Copyright 1998
    304 Pages
    by Chapman & Hall

    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.

    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

    Biography

    Jerzy Szulga is Professor of Mathematics at Auburn University in Alabama, US.

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