Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastic Calculus: 1865 (Lecture Notes in Mathematics)

by David Applebaum (Author), Michael Schuermann (Editor), David Applebaum (Author), Michael Schuermann (Editor), Uwe Franz (Editor), B.V. Rajarama Bhat (Contributor), J. Martin Lindsay (Contributor), Johan Kustermans (Contributor)

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Illustrated
2005
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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: Levy 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.

Synopsis

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: Levy 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.

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More Information

Format: Illustrated
Pages: 324
Edition: 2005
Publisher: Springer
Published: 18 Feb 2005
ISBN 10: 3540244069
ISBN 13: 9783540244066

Author Bio

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 Levy processes and stochastic flows on manifolds driven by Levy type noise. Earlier this year he published a monograph on Levy 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.