---------- Forwarded message ---------- From: Walter Schachermayer ---------- Forwarded message ---------- Date: Fri, 23 Jun 2006 10:46:41 +0200 From: Annette Weihs annette.weihs@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@oeaw.ac.at http://www.ricam.oeaw.ac.at