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An Innovation Approach To Random Fields

Application Of White Noise Theory

An Innovation Approach To Random Fields by Takeyuki Hida
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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.

World Scientific Publishing Company; January 2004
204 pages; ISBN 9789814487924
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Title: An Innovation Approach To Random Fields
Author: Takeyuki Hida