AN INNOVATION APPROACH TO RANDOM FIELDS
Application of White Noise Theory
by Takeyuki Hida (Meijo University, Japan) & Si Si (Aichi Prefectural University, Japan)
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.
Contents:
- Introduction
- White Noise
- Poisson Noise
- Random Fields
- Gaussian
Random Fields
- Some Non-Gaussian Random Fields
- Variational Calculus for Random Fields
- Innovation Approach
- Reversibility
- Applications
Readership: Graduate students and researchers in pure and applied mathematics,
as well as theoretical physicists.
“This nice book synthesizes recent contributions of the authors to the significant issue of innovation in random systems.”
“This book contains many references to the literature, with small examples containing open ends and suggestions, and may hence provide the starting point for further research.”
| 204pp |
Pub. date: Jul 2004 |
