Innovation Approach To Random Fields, An: Application Of White Noise Theory
Application of White Noise Theory
- 204 pages
- English
- PDF
- Available on iOS & Android
Innovation Approach To Random Fields, An: Application Of White Noise Theory
Application of White Noise Theory
About This Book
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.
Frequently asked questions
Information
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