Lecture Notes in Mathematics

Quantum Independent Increment Processes I

From Classical Probability to Quantum Stochastic Calculus

Authors: Applebaum, D., Bhat, B.V.R., Kustermans, J., Lindsay, J.M.

Editors: Schuermann, Michael, Franz, Uwe (Eds.)

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About this book

This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics.

The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

About the authors

The four lecturers are all established experts in their area.

In the eighties, D. Applebaum was one of the pioneers of quantum stochastic calculus, where he introduced quantum stochastic integration based on Fermionic white noise. He now works on classical Lévy processes and stochastic flows on manifolds driven by Lévy type noise. Earlier this year he published a monograph on Lévy processes with Cambridge University Press.

J. Kustermans developed together with Stefan Vaes the definition of a locally compact quantum group which has now become generally accepted.

J.M. Lindsay is one of the most prominent representatives of the Nottingham quantum probability school which was founded by Robin Hudson, the inventor (with K.R. Parthasarathy) of quantum stochastic calculus.

B.V.R. Bhat is a student of K.R. Parthasarathy, one of the founders of quantum stochastic calculus. In 1997, B.V.R. Bhat received the INSA Medal for Young Scientist by the Indian National Science Academy, New Dehli.

Table of contents (4 chapters)

  • Lévy Processes in Euclidean Spaces and Groups

    Applebaum, David

    Pages 1-98

  • Locally compact quantum groups

    Kustermans, Johan

    Pages 99-180

  • Quantum Stochastic Analysis – an Introduction

    Lindsay, J. Martin

    Pages 181-271

  • Dilations, Cocycles and Product Systems

    Bhat, B. V. Rajarama

    Pages 273-291

Buy this book

eBook £40.99
price for United Kingdom (gross)
  • ISBN 978-3-540-31450-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £51.99
price for United Kingdom (gross)
  • ISBN 978-3-540-24406-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Independent Increment Processes I
Book Subtitle
From Classical Probability to Quantum Stochastic Calculus
Authors
Editors
  • Michael Schuermann
  • Uwe Franz
Series Title
Lecture Notes in Mathematics
Series Volume
1865
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31450-9
DOI
10.1007/b105131
Softcover ISBN
978-3-540-24406-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVIII, 299
Topics