© 2005

Quantum Independent Increment Processes I

From Classical Probability to Quantum Stochastic Calculus

  • Editors
  • Michael Schürmann
  • Uwe Franz

Part of the Lecture Notes in Mathematics book series (LNM, volume 1865)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Johan Kustermans
    Pages 99-180
  3. J. Martin Lindsay
    Pages 181-271
  4. B. V. Rajarama Bhat
    Pages 273-291
  5. Back Matter
    Pages 293-299

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.


Lévy process Lévy processes Stochastic calculus compressions and dilations mathematical physics quantum dynamical semigroups quantum groups quantum stochastic calculus

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.

Bibliographic information

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