Wolfhard Hansen, Martina Zhle
Restricting isotropic α-stable Lévy processes from
to fractal sets
The restriction of an isotropic α-stable Lévy process Xα in ℝn on the fractal support F of certain finite Borel measures μ is introduced in three different ways: by means of the trace of its Dirichlet form on F and related Besov spaces, by its μ-local time on F and the corresponding time changed process, and by restricting on the fine support of μ via balayage spaces and potentials.
Moreover, for compact upper d-regular sets F with d > n − α an approximation by means of restrictions of Xα to small ϵ-neighborhoods of F is given.
Forum Mathematicum, Walter de Gruyter
Print ISSN: 0933-7741
Volume: 18, 03/2006
Pages: 171 - 191
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