Summary and Info
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.
More About the Author
Takayuki Hida (肥田隆行, Hida Takayuki, born May 4, 1944) is a retired Japanese speed skater. He competed at the 1968 and 1972 Winter Olympics in the 500 m events and finished in 37th and 13th place, respectively.
Review and Comments
Rate the Book
An innovation approach to random fields: application of white noise theory 0 out of 5 stars based on 0 ratings.