Innovation Approach To Random Fields, An: Application Of White Noise Theory

Application of White Noise Theory

Takeyuki Hida, Si Si

• Publisher: World Scientific
• Year: 2004
• Print ISBN: 9789812380951, 9789812380951
• eBook ISBN: 9789812565389
• Topic: Matemáticas
• Subtopic: Matemática aplicada

A random field is a mathematical model of evolutional fluctuating complex systems parametrized by a multi-dimensional manifold like a curve or a surface. As the parameter varies, the random field carries much information and hence it has complex stochastic structure.The authors of this book use an approach that is characteristic: namely, they first construct innovation, which is the most elemental stochastic process with a basic and simple way of dependence, and then express the given field as a function of the innovation. They therefore establish an infinite-dimensional stochastic calculus, in particular a stochastic variational calculus. The analysis of functions of the innovation is essentially infinite-dimensional. The authors use not only the theory of functional analysis, but also their new tools for the study.

Table of contents

• Contents
• Preface
• 1. Introduction
• 2. White Noise
• 3. Poisson Noise
• 4. Random Fields
• 5 Gaussian Random Fields
• 6 Some Non-Gaussian Random Fields
• 7 Variational Calculus For Random Fields
• 8 Innovation Approach
• 9 Reversibility
• 10 Applications
• Appendix
• Epilogue
• List of Notations
• Bibliography
• Index