---------- Forwarded message ----------
From: Walter Schachermayer
---------- Forwarded message ----------
Date: Fri, 23 Jun 2006 10:46:41 +0200
From: Annette Weihs <annette.weihs(a)oeaw.ac.at>
Subject: [Ricam-all] RICAM-Colloquia
Prof. Jozef Teugels
Katholieke Universiteit Leuven
Monday, July 24, 14:00, HF136
Title: Levy Processes, Polynomials and Martingales
Abstract: It has long been known that there is a close relationship between
Brownian motion {W(t),t>=0} and the Hermite polynomials {Hm(y),m=0,1,..}.
More specifically E{H_m(W(t)/Sqrt{2t})| W(s)}= (s/t)^(m/2)
H_m(W(s)/Sqrt{2s}).
We show that a similar property holds for a large variety of pairs of Levy
processes and polynomials associated with them. Particular attention is
given to orthogonal polynomials. Apart from the well-known case of Brownian
motion, the Poisson process (with the Charlier poly-nomials) and the
Bernoulli process (with the Krawtchouck poly-nomials) provide two other
explicit examples.
This work is joint with Wim Schoutens of the K.U. Leuven (Belgium).
Annette Weihs
Johann Radon Institute for Computational
and Applied Mathematics (RICAM)
Austrian Academy of Sciences
Altenbergerstr. 69
A-4040 Linz
Tel.: +43 (0)732 2468-5211
Fax: +43 (0)732 2468-5212
e-mail: annette.weihs(a)oeaw.ac.at
http://www.ricam.oeaw.ac.at