Lévy processes : theory and applications
著者
書誌事項
Lévy processes : theory and applications
Birkhäuser, c2001
- : Boston
- : Basel
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注記
Includes bibliographical references
内容説明・目次
内容説明
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. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Levy 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 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. 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 Levy processes.
目次
Preface
I. A tutorial on Levy processes
Sato, K.: Basic results on Levy 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 Levy processes
Watanabe, T.: Temporal change in distributional properties of Levy processes
III: Extensions and generalisations of Levy processes
Applebaum, D.: Levy processes in stochastic differential geometry
Jac. / Schilling, R.L.: Levy-type processes and pseudo-differential operators
Maejima, M.: Semi-stable distributions
IV. Applications in physics
Albeverio, S. / Rudiger, B. / Wu, J-L.: Analytic and probabilistic aspects of Levy processes and fields in quantum theory
Holevo, A.S.: Levy processes and continuous quantum measurements
Woyczynski, W.A.: Levy 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 Levy processes for financial econometrics
Eberlein, E.: Application of generalized hyperbolic Levy 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 Levy processes from the perspective of point processes
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