Synopses & Reviews
This monograph presents a framework for infinite dimensional analysis based on white noise. This approach, which has many areas of application is both intuitive and efficient. Among the concepts and structures generalized to an infinite dimensional setting in this book are: spaces of test and generalized functions, differential calculus, Laplacian and Fourier transforms and Dirichlet forms and their Markov processes. A multitude of concepts, such as Brownian motion functionals, falls into this framework. This book presents a simple, yet general theory of stochastic integration and also discusses construction quantum field theory and Feynman's functional integration. This volume will be of interest to mathematicians and scientists who use stochastic methods in their research. The book will be of particular value to mathematicians in probability theory, functional analysis, measure theory, potential theory, as well as to physicists and scientists in engineering.
Synopsis
Gives a framework for infinite dimensional analysis based on white noise. Among the concepts and structures generalized to an infinite dimensional setting in this book are: spaces of test and generalized functions, differential calculus and Laplacian and Fourier transforms.
Table of Contents
Preface. Notations and Convention.
1. Gaussian Spaces.
2. T and
S Transformation and the Decomposition Theorem.
3. Generalized Functionals.
4. The Spaces (S) and (
S)*.
5. Calculus of Differential Operators.
6. Laplacian Operators.
7. The Spaces
D and
D*.
8. Stochastic Integration.
9. Fourier and Fourier-Mehler Transforms.
10. Dirichlet Forms.
11. Applications to Quantum Field Theory.
12. Feynman Integrals. Appendices. Bibliography.