Alexander Schnurr (Dortmund):
On the Natural Appearance of Continuous Negative Definite Functions in the Analysis of Stochastic Processes
Time and place
Thursday, 23.4.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
Continuous negative definite functions in the sense of Schoenberg appear\nin various parts of modern mathematics. One example is\npotential theory on locally compact Abelian groups. In the theory of\nstochastic processes it is well known that with each Lévy process one\nassociates a function of this class and that this relationship is in a\ncertain sense 1:1. In this talk, we analyze other occasions where\ncontinuous negative definite functions show up, namely in the context of\nFeller processes as well as homogeneous diffusions with jumps. We give\nan overview on the applications or theses functions in analyzing path\nand distributional properties of the processes under consideration.\n\nBibliography:\n\n[1] Behme, A. and Schnurr, A. (2014+): A Criterion for Invariant\nMeasures of Itô Processes Based on the Symbol. To appear in Bernoulli.\n\n[2] Schnurr, A. (2013): Generalization of the Blumenthal-Getoor Index to\nthe Class of Homogeneous Diffusions with Jumps and Some Applications.\nBernoulli 19(5A) (2013), 2010-2032.\n