White Noise on Bialgebras

  • Authors
  • Michael Schürmann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1544)

Table of contents

  1. Front Matter
    Pages I-V
  2. Michael Schürmann
    Pages 1-11
  3. Michael Schürmann
    Pages 12-40
  4. Michael Schürmann
    Pages 41-68
  5. Michael Schürmann
    Pages 69-80
  6. Michael Schürmann
    Pages 81-113
  7. Michael Schürmann
    Pages 128-137
  8. Back Matter
    Pages 138-146

About this book

Introduction

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.

Keywords

Hopf Algebras Martingale Probability theory Quantum Probability Quantum Stochastic Calculus Stochastic processes White Noise algebra differential equation functional analysis stochastic process

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0089237
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56627-4
  • Online ISBN 978-3-540-47614-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book