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Stochastic Analysis and Random Maps in Hilbert Space (Hardcover, Reprint 2018)
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Stochastic Analysis and Random Maps in Hilbert Space (Hardcover, Reprint 2018)
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01/07 This title is now available from Walter de Gruyter. Please
see www.degruyter.com for more information. This book is devoted to
stochastic operators in Hilbert space. A number of models in modern
probability theory apply the notion of a stochastic operator in
explicit or latent form. In this book, objects from the Gaussian
case are considered. Therefore, it is useful to consider all random
variables and elements as functionals from the Wiener process or
its formal derivative, i.e. white noise. The book consists of five
chapters. The first chapter is devoted to stochastic calculus and
its main goal is to prepare the tools for solving stochastic
equations. In the second chapter the structure of stochastic
equations, mainly the structure of Gaussian strong linear
operators, is studied. In chapter 3 the definition of the action of
the stochastic operator on random elements in considered. Chapter 4
deals with the mathematical models in which the notions of
stochastic calculus arise and in the final chapter the equation
with random operators is considered.
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