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.
- ISBN10 1281876968
- ISBN13 9781281876966
- Publish Date 1 January 2004
- Publish Status Active
- Out of Print 17 February 2015
- Publish Country US
- Imprint World Scientific Publishing Company
- Format eBook
- Pages 189
- Language English