Universita' degli Studi di Bologna - Facolta' di Scienze
DIPARTIMENTO DI FISICA -- DOTTORATO DI RICERCA IN FISICA
Anno Accademico 1999/200
SEMINAR ANNOUNCEMENT
Rudolf GORENFLO
Emeritus Professor at the Free University of Berlin,
Department of Mathematics and Computing Sciences
FRACTIONAL DIFFUSION PROCESSES AND RANDOM WALK MODELS
GIOVEDI' 4 Novembre '99 ore 14:30-15:30
AULA D, Dipartimento di Fisica, Via Irnerio 46, 40126 BOLOGNA
Abstract
By replacing in the common one-dimensional diffusion equation the
second-order spatial derivative by a special (symmetric or non-symmetric)
fractional derivative as done by Feller (1952), one obtains as Green
function a L\'evy stable probability density evolving in time. The resulting
evolution processes are Markovian: we call them "L\'evy-Feller diffusion".
Special cases are the Gauss and the Cauchy processes.
We present some random walk models, discrete in space and time,
which,
for properly scaled transition to vanishing space and time steps, converge
in
distribution to the corresponding time-parameterized stable distribution.
We also present an approximating random walk scheme, continuous in space and
discrete in time, which is very convenient to simulate stable stochastic
processes in view of Gnedenko's limit theorem.
Finally, we briefly discuss the time-fractional diffusion equation
(first-time derivative replaced by a special fractional derivative), which
leads to a non-Markovian stochastic process and a peculiar random walk model
to be compared with the fractional Brownian motion.
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For futher informations, please contact Prof. F. Mainardi,
Dipartimento di Fisica, Uff. 236, Via Irnerio 46, 40126 BOLOGNA
Tel: 051-20-91098, e-mail:[log in to unmask]
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