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.
- ISBN13 9789814713580
- Publish Date 31 October 2018
- Publish Status Active
- Publish Country SG
- Imprint World Scientific Publishing Co Pte Ltd
- Format Hardcover
- Pages 300
- Language English
- URL http://worldscientific.com/worldscibooks/10.1142/9742