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Licensed Unlicensed Requires Authentication Published by De Gruyter May 17, 2006

Restricting isotropic α-stable Lévy processes from to fractal sets

  • Wolfhard Hansen EMAIL logo and Martina Zähle
From the journal

Abstract

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 ɛ-neighborhoods of F is given.


(Communicated by Masatoshi Fukushima)


Received: 2004-01-13
Accepted: 2004-05-21
Published Online: 2006-05-17
Published in Print: 2006-03-21

© Walter de Gruyter

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