Lévy Processes
Theory and Applications
(Sprache: Englisch)
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,...
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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.
Inhaltsverzeichnis zu „Lévy Processes “
PrefaceI. A tutorial on Lévy processesSato, K.: Basic results on Lévy processesII. Distributional, pathwise and structural resultsCarmona, P. / Petit, F. / Yor, M.: Exponentials functionals of Levy processesDoney, R.: Fluctuation theory for Levy processesMarcus, M.B. / Rosen, J.: Gaussian processes and the local times of symmetric Lévy processesWatanabe, T.: Temporal change in distributional properties of Lévy processesIII: Extensions and generalisations of Lévy processesApplebaum, D.: Lévy processes in stochastic differential geometryJac. / Schilling, R.L.: Lévy-type processes and pseudo-differential operatorsMaejima, M.: Semi-stable distributionsIV. Applications in physicsAlbeverio, S. / Rüdiger, B. / Wu, J-L.: Analytic and probabilistic aspects of Lévy processes and fields in quantum theoryHolevo, A.S.: Lévy processes and continuous quantum measurementsWoyczynski, W.A.: Lévy processes in the physical sciencesBertoin, J.: Some properties of Burgers turbulence with white or stable noiseV. Applications in financeBarndorff-Nielsen, O.E / Shepard, N.: Modelling by Lévy processes for financial econometricsEberlein, E.: Application of generalized hyperbolic Lévy motions to financeMa, J. / Protter, P. / Zhang, J: Explicit form and path regularity of martingale representationYor, M.: Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuityVI. Numerical and statistical aspectsNolan, J.P.: Maximum likelihood estimation and diagnostics for stable distributionsRosinski, J.: Series representations of Lévy processes from the perspective of point processes
Bibliographische Angaben
- 2012, Softcover reprint of the original 1st ed. 2001., 418 Seiten, Maße: 17,8 x 25,4 cm, Kartoniert (TB), Englisch
- Herausgegeben von Barndorff-Nielsen, Ole E; Mikosch, Thomas; Resnick, Sidney I.
- Herausgegeben: Thomas Mikosch, Sidney I. Resnick, Ole E Barndorff-Nielsen
- Verlag: Springer
- ISBN-10: 1461266572
- ISBN-13: 9781461266570
- Erscheinungsdatum: 23.10.2012
Sprache:
Englisch
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