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Diffusion on locally compact ultrametric spaces. (English) Zbl 1151.60303

Summary: We consider an ultrametric space with sufficiently many isometries and we construct a class of diffusion processes on the space as appropriate limits of discrete processes on the (open and closed) balls of the space. We show, using a version of the Lévy Khintchine formula adapted to this general context, that our construction includes all convolution semigroups associated to an unbounded Lévy measure. Finally we relate our construction to the construction of diffusion processes due to S. Albeverio and W. Karwowski [Ser. Probab. Stat. 1, 86–99 (1991; Zbl 0826.46069)] on \(p\)-adic fields.

MSC:

60B05 Probability measures on topological spaces
43A85 Harmonic analysis on homogeneous spaces
43A90 Harmonic analysis and spherical functions
60J60 Diffusion processes

Citations:

Zbl 0826.46069
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References:

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