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

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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.