Lecture Notes in Mathematics

White Noise on Bialgebras

Authors: Schürmann, Michael

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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.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Pages 1-11

    Schürmann, Michael

  • Basic concepts and first results

    Pages 12-40

    Schürmann, Michael

  • Symmetric white noise on Bose Fock space

    Pages 41-68

    Schürmann, Michael

  • Symmetrization

    Pages 69-80

    Schürmann, Michael

  • White noise on bose fock space

    Pages 81-113

    Schürmann, Michael

Buy this book

eBook $24.99
price for USA in USD
  • ISBN 978-3-540-47614-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $33.00
price for USA in USD
  • ISBN 978-3-540-56627-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
White Noise on Bialgebras
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1544
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47614-6
DOI
10.1007/BFb0089237
Softcover ISBN
978-3-540-56627-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VI, 146
Topics