An innovation approach to random fields: application of white noise theory

✍ Scribed by Takeyuki Hida, Si Si

• Book ID: 127426406
• Publisher: World Scientific
• Year: 2004
• Tongue: English
• Weight: 1 MB
• Category: Library
• City: River Edge, NJ
• ISBN: 9812565388

✦ Synopsis

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.