Introduction to Hida distributions

Includes index

Includes bibliography (p. 243-249) and references.

Preliminaries and Discrete Parameter White Noise
Continuous Parameter White Noise
1.White Noise Functional
2. White Noise Analysis
3.Stochastic Integral
4.Gaussian and Poisson Noises
5.Multiple Markov Properties of Generalized Gaussian Processes and Generalizations
6.Classification of Noises
7.Lévy Processes

This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.