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White Noise on Bialgebras

  • Book
  • © 1993

Overview

Authors:
  1. Michael Schürmann
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1544)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Michael Schürmann
    Pages 1-11

  3. Basic concepts and first results

    • Michael Schürmann
    Pages 12-40

  4. Symmetric white noise on Bose Fock space

    • Michael Schürmann
    Pages 41-68

  5. Symmetrization

    • Michael Schürmann
    Pages 69-80

  6. White noise on bose fock space

    • Michael Schürmann
    Pages 81-113

  7. Quadratic components of conditionally positive linear functionals

    • Michael Schürmann
    Pages 114-127

  8. Limit theorems

    • Michael Schürmann
    Pages 128-137

  9. Back Matter

    Pages 138-146
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Keywords

About this book

Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory.

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