Lévy Processes: Theory and Applications

ISBN-13: 9780817641672 / Angielski / Twarda / 2001 / 418 str.

OLE Barndorff-Nielsen; OLE E. Barndorff-Nielsen; Thomas Mikosch

Opis

A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. 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 Levy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Levy 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. It collects articles written by leading experts that will appeal to the non-specialist. 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 future research. 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 Levy processes.

Recenzje

"This volume presents a useful summary of some of the recent scientific developments concerning Lévy processes. Both introductory and more advanced articles are included. The interested researcher will get a good overview of 'where the action is' whereas students will find numerous interesting research topics to work on . . . I am convinced that the text will contribute further to making stochastic models based on general Lévy processes even more popular. I, therefore, take pleasure in recommending this volume to all interested readers." -ISI Short Book Reviews

Spis treści

Preface I. A tutorial on Lévy processes Sato, K.: Basic results on Lévy processes II. Distributional, pathwise and structural results Carmona, P. / Petit, F. / Yor, M.: Exponentials functionals of Levy processes Doney, R.: Fluctuation theory for Levy processes Marcus, M.B. / Rosen, J.: Gaussian processes and the local times of symmetric Lévy processes Watanabe, T.: Temporal change in distributional properties of Lévy processes III: Extensions and generalisations of Lévy processes Applebaum, D.: Lévy processes in stochastic differential geometry Jac. / Schilling, R.L.: Lévy-type processes and pseudo-differential operators Maejima, M.: Semi-stable distributions IV. Applications in physics Albeverio, S. / Rüdiger, B. / Wu, J-L.: Analytic and probabilistic aspects of Lévy processes and fields in quantum theory Holevo, A.S.: Lévy processes and continuous quantum measurements Woyczynski, W.A.: Lévy processes in the physical sciences Bertoin, J.: Some properties of Burgers turbulence with white or stable noise V. Applications in finance Barndorff-Nielsen, O.E / Shepard, N.: Modelling by Lévy processes for financial econometrics Eberlein, E.: Application of generalized hyperbolic Lévy motions to finance Ma, J. / Protter, P. / Zhang, J: Explicit form and path regularity of martingale representation Yor, M.: Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity VI. Numerical and statistical aspects Nolan, J.P.: Maximum likelihood estimation and diagnostics for stable distributions Rosinski, J.: Series representations of Lévy processes from the perspective of point processes