An Innovation Approach to Random Fields: Application of White Noise Theory

Front Cover
World Scientific, 2004 - Mathematics - 204 pages
0 Reviews
A random field is a mathematical model of evolutional fluctuatingcomplex systems parametrized by a multi-dimensional manifold like acurve or a surface. As the parameter varies, the random field carriesmuch 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 elementalstochastic process with a basic and simple way of dependence, and thenexpress the given field as a function of the innovation. Theytherefore establish an infinite-dimensional stochastic calculus, inparticular a stochastic variational calculus. The analysis offunctions of the innovation is essentially infinite-dimensional. Theauthors use not only the theory of functional analysis, but also theirnew tools for the study
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
5 Of course there are many applications where a person can receive
5
and we may say that the book is elemental but not elementary However
11
Poisson Noise
33
Random Fields
55
Gaussian Random Fields
65
Some NonGaussian Random Fields
85
Variational Calculus for Random Fields
97
Reversibility
143
Applications
151
Appendix
163
Appendix 3
171
Epilogue
177
T Hida and Si
178
Index
187
Copyright

Innovation Approach
117

Other editions - View all

Common terms and phrases

Bibliographic information