Ole E Barndorff-Nielsen

K. Hutter

Brian B. Willetts

F. Ziegler

C. Christiansen

J.C.R. Hunt

J.T. Moller

K.R. Rasmussen

M. Sorensen

Wind erosion has such a pervasive influence on environmental and agricultural matters that academic interest in it has been continuous for several decades. However, there has been a tendency for the resulting publications to be scattered widely in the scientific litera ture and consequently to provide a less coherent resource than might otherwise be hoped for. In particular, cross-reference between the literature on desert and coastal morphology, on the deterioration of wind affected soils, and on the process mechanics of the grain/air flow system has been disappointing. A successful workshop on "The Physics of Blown Sand", held in Aarhus in 1985, took a decisive step in collecting a research community with interests spanning geomorphology and grain/wind process mechanics. The identification of that Community was reinforced by the Binghampton Symposium on Aeolian Geomorphology in 1986 and has been fruitful in the development of a number of international collaborations. The objectives of the pre sent workshop, which was supported by a grant from the NATO Scientific Affairs Division, were to take stock of the progress in the five years to 1990 and to extend the scope of the community to include soil deterioration (and dust release) and those beach processes which link with aeolian activity on the coast.

The Erosional Environment

Aeolian Grain Transport

Uwe Franz

Rolf Gohm

Burkhard Kümmerer

Steen Thorbjørnsen

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.

Structure of Quantum Lévy Processes, Classical Probability, and Physics

Quantum Independent Increment Processes II

Brian B Willetts

Aeolian Grain Transport 1

Sidney I. Resnick

Thomas Mikosch

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Theory and Applications

Lévy Processes

Albert Shiryaev

Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.

Second Edition

Change of Time and Change of Measure

Ole E Barndorff-Nielsen

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