Lévy Processes: Theory and ApplicationsOle E BarndorffNielsen, Thomas Mikosch, Sidney I. Resnick A Lévy process is a continuoustime 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 stateoftheart of this rapidly evolving subject with special emphasis on the nonBrownian 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.

What people are saying  Write a review
Contents
III  3 
IV  39 
V  41 
VI  57 
VII  67 
VIII  89 
IX  109 
X  111 
XV  225 
XVI  241 
XVII  267 
XVIII  281 
XIX  283 
XX  319 
XXI  337 
XXII  361 