Overview

We propose a new direction for stochastic analysis. Starting with a noise which is a system of i.i.d. idealized elemental random variables, we form polynomials in the noise and come to the space of generalized functionals of the noise with special emphasis on the Gaussian noise. New tools of analyzing these functionals are introduced. We further establish a harmonic analysis arising from the infinite dimensional rotation group which plays significant roles in white noise analysis. Many applications, in particular to quantum dynamics, have been shown.Functionals of other kind of noises are discussed. As a new approach, we discuss functionals of a space noise. There one can find similarity and dissimilarity as well as duality to the analysis of Poisson noise functionals.

Full Product Details

Author:   Takeyuki Hida (Nagoya Univ & Meijo Univ, Japan) ,  Si Si (Aichi Prefectural Univ, Japan & Yangon Univ, Myanmar)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
ISBN:  

9789814713580

ISBN 10:   9814713589
Pages:   300
Publication Date:   31 October 2018
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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