Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastic Calculus / Edition 1

by David Applebaum, Michael Schuermann, B.V. Rajarama Bhat, Uwe Franz, Johan Kustermans

Overview

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 Shastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Product Details

ISBN-13:	9783540244066
Publisher:	Springer Berlin Heidelberg
Publication date:	04/06/2005
Series:	Lecture Notes in Mathematics , #1865
Edition description:	2005
Pages:	299
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

The four lecturers are all established experts in their area.

In the eighties, D. Applebaum was one of the pioneers of quantum shastic calculus, where he introduced quantum shastic integration based on Fermionic white noise. He now works on classical Lévy processes and shastic 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 shastic calculus.

B.V.R. Bhat is a student of K.R. Parthasarathy, one of the founders of quantum shastic 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

Lévy Processes in Euclidean Spaces and Groups.- Locally Compact Quantum Groups.- Quantum Shastic Analysis - an Introduction.- Dilations, Cocycles and Product Systems.