Quantum Independent Increment Processes I

This volume is the first of two volumes containing the revised and completed notes lectures given at the school &quote;Quantum Independent Increment Processes: Structure and Applications to Physics&quote;. 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: &quote;Levy Processes in Euclidean Spaces and Groups&quote; by David Applebaum, &quote;Locally Compact Quantum Groups&quote; by Johan Kustermans, &quote;Quantum Stochastic Analysis&quote; by J. Martin Lindsay, and &quote;Dilations, Cocycles and Product Systems&quote; by B.V. Rajarama Bhat.