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Collecting together twenty-three self-contained articles, this volume presents the current research of a number of renowned scientists in both probability theory and statistics as well as their various applications in economics, finance, the physics of wind-blown sand, queueing systems, risk assessment, turbulence and other areas. The contributions are dedicated to and inspired by the research of Ole E. Barndorff-Nielsen who, since the early 1960s, has been and continues to be a very active and influential researcher working on a wide range of important problems. The topics covered include, but are not limited to, econometrics, exponential families, Lévy processes and infinitely divisible distributions, limit theory, mathematical finance, random matrices, risk assessment, statistical inference for stochastic processes, stochastic analysis and optimal control, time series, and turbulence. The book will be of interest to researchers and graduate students in probability, statistics and their applications.  .

Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical statistics. --- Probabilities. --- Probability --- Statistical inference --- Statistics, Mathematical --- Statistical methods --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution (Probability theory. --- Finance. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Statistical Theory and Methods. --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Economics, Mathematical . --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Mathematical economics --- Methodology

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This is the second of two volumes containing the revised and completed notes of 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 in March, 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 second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.

Mathematics. --- Distribution (Probability theory). --- Mathematical physics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Mathematical and Computational Physics. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical Theory --- Physical mathematics --- Physics --- Distribution functions --- Frequency distribution --- Math --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Physics. --- Theoretical, Mathematical and Computational Physics. --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- Distribution (Probability theory. --- Characteristic functions --- Probabilities --- Stochastic analysis. --- Probabilistic number theory. --- Lévy processes. --- Random walks (Mathematics) --- Number theory --- Analysis, Stochastic --- Stochastic processes --- Distribution (Probability theory) --- Probability Theory.