Lectures on White Noise Functionals

' White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications. Contents:Generalized White Noise FunctionalsElemental Random Variables and Gaussian ProcessesLinear Processes and Linear FieldsHarmonic Analysis Arising from Infinite Dimensional Rotation GroupComplex White Noise and Infinite Dimensional Unitary GroupCharacterization of Poisson NoiseInnovation TheoryVariational Calculus for Random Fields and Operator FieldsFour Notable Roads to Quantum Dynamics Readership: Researchers in probability and statistics and mathematical physics. Keywords:White Noise;Poisson Noise;Stochastic Analysis;Innovation;Random Field and Its Variation;Random Complexity;Infinite Dimensional Rotation GroupKey Features:A tightly edited distillation of a quarter of century of work by many scientistsContains the original ideas with some interpretation of development to recent worksCommentaries on each of the topics coveredReviews:“This monograph is a valuable guide to the world of white noise analysis originated by Hida. It is full of ideas, essentials and philosophy about why analysis based upon the white noise is needed, what the white noise functionals are, how to handle stochastic processes on an applicational basis to quantum physics, how to find a natural way to formulate the infinite-dimensional harmonic analysis, etc. This book is recommendable not only to ambitious graduate students in probability or applied analysis in a broad sense, but also to researchers who work on infinite-dimensional analysis or mathematical physics, as well as to any readers who are interested in white noise analysis.”Mathematical Reviews '