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Host: MaPhySto, University of Aarhus
Homepage: http://www.maphysto.dk/events/LevyCAC2000/
Organizers: Goran Peskir
Description:
Lévy processes are stochastic processes on the Euclidean space, stochastically continuous and with stationary independent
increments. Examples are Brownian motion, Poisson processes, stable processes (such as Cauchy processes), and
subordinators (such as Gamma-processes). They form a basic class in stochastic analysis. This course aims at giving an
introduction to elementary properties of Lévy process and to transformations between Lévy processes. Familiarity with the
method of characteristic functions and some knowledge of Brownian motion, Poisson processes, and infinitely divisible
distributions are expected. The following are the main contents of the lectures.
1.Characterization of Lévy processes by the Lévy-Khintchine representation of infinitely divisible distributions. Probabilistic meaning of the characterization. 2.Transformations of Lévy processes to Lévy processes. Especially, the subordination invented by Bochner and the density transformation (mutual absolute continuity in the path space in finite time) of Skorohod, Newman, and Kunita-S.Watanabe will be discussed in detail. 3.Large time behaviors of Lévy processes. Especially recurrence, transience, and oscillation are characterized. (Chung-Fuchs, Spitzer, Port-Stone, Shepp, Kesten, Erickson) 4.Time evolution of unimodality and multimodality of the distributions of Lévy processes on the line. (Wolfe, Yamazato, Sato, Toshiro Watanabe)
The following forthcoming book will be a reference: K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, to appear in autumn, 1999.
Speakers: Ken-iti Sato (Nagoya University), Francesco Mainardi (University of Bologna)
Date received: October 07, 1999
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