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.

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Keywords Degree, Degree of recurrence, Degree of transience, Hierarchical group, Hierarchical random walk, k-strong transience, Multilevel branching system, Occupation time, Separation of time scales, Ultrametric space
Persistent URL
Journal Potential Analysis
Dawson, D.A, Gorostiza, L.G., & Wakolbinger, A. (2005). Degrees of transience and recurrence and hierarchical random walks. Potential Analysis, 22(4), 305–350. doi:10.1007/s11118-004-1327-6