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.

Sommario

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

Dettagli sul prodotto

• Autori: Takeyuki Hida, Hida Takeyuki, Si Si, Si Si, Hida Takeyuki
• Editore: World Scientific Publishing
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 01.01.2004
• EAN: 9789812380951
• ISBN: 978-981-238-095-1
• Pagine: 189
• Peso: 404 g
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Teoria delle probabilità, stocastica, statistica matematica; Algebra, MATHEMATICS / Applied, MATHEMATICS / Differential Equations / General, MATHEMATICS / Complex Analysis, Stochastics