(1) Carleton University, Ottawa, Canada, K1S 5B6;(2) Centro de Investigación y de Estudios Avanzados, 07000 México, D.F., Mexico;(3) Goethe-Universität, Frankfurt am Main, Germany
Abstract:
The notion of degree and related notions concerning recurrence and transience for a class of Lévy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is examined with emphasis on the role of the ultrametric structure of the group and on analogies and differences with Euclidean random walks. Applications to separation of time scales and occupation times of multilevel branching systems are discussed.Mathematics Subject Classifications (2000) 60G50, 60B15, 60F05, 60J80.D.A. Dawson: Research supported by NSERC (Canada) and a Max Planck Award for International Cooperation.L.G. Gorostiza: Research supported by CONACYT grant 37130-E (Mexico).A. Wakolbinger: Research supported by DFG (SPP 1033) (Germany).
