INNOVATION APPROACH TO RANDOM FIELDS, AN: APPLICATION OF WHITE NOISE THEORY

Hida, Takeyuki,Si, Si

ISBN 10: 9812380957 / ISBN 13: 9789812380951

Edité par World Scientific Publishing Comp, 2004

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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.

Présentation de l'éditeur: “This nice book synthesizes recent contributions of the authors to the significant issue of innovation in random systems.” Mathematical Reviews “This book contains many references to the literature, with small examples containing open ends and suggestions, and may hence provide the starting point for further research.” Zentralblatt Math 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.

Détails bibliographiques

Titre : INNOVATION APPROACH TO RANDOM FIELDS, AN: ...
Éditeur : World Scientific Publishing Comp
Date d'édition : 2004
Reliure : hardcover
Etat : Very Good