Innovation Approach To Random Fields, An: Application Of White Noise Theory
By: Si Si (author), Takeyuki Hida (author)Hardback
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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.
Background; Probabilistic Properties of Random Fields; Gaussian Random Fields; Some Non-Gaussian Random Fields; Variational Calculus for Random Fields; Innovation Approach; Reversibility; Applications.
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- ID: 9789812380951
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