Home Browse by Subject Bestsellers New Titles Editor's Choice New Reviews Textbooks
Search Book Series Study Guides Rights Inspection Copy Contact Us Join Our Mailing List
For Authors How to Order E-Catalogues

Browse all Subjects
Search Bookshop
New Titles
Editor's Choice
Bestsellers
Book Series
Textbooks
Journals
Join Our Mailing List
 
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.”

Mathematical Reviews





“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.”

Zentralblatt MATH




204pp Pub. date: Jul 2004
ISBN 978-981-238-095-1
981-238-095-7
US$75 / £55


Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 5 September 2008