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

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.

List of contents

Background; Probabilistic Properties of Random Fields; Gaussian Random Fields; Some Non-Gaussian Random Fields; Variational Calculus for Random Fields; Innovation Approach; Reversibility; Applications.

Product details

• Authors: Takeyuki Hida, Hida Takeyuki, Si Si, Si Si, Hida Takeyuki
• Publisher: World Scientific Publishing
• Languages: English
• Product format: Hardback
• Released: 01.01.2004
• EAN: 9789812380951
• ISBN: 978-981-238-095-1
• No. of pages: 189
• Weight: 404 g
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Algebra, MATHEMATICS / Applied, MATHEMATICS / Differential Equations / General, MATHEMATICS / Complex Analysis, Stochastics