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