Journal of Theoretical Probability

, Volume 32, Issue 2, pp 765–780 | Cite as

The Hausdorff dimension of the range of the Lévy multistable processes

  • R. Le GuévelEmail author


We compute the Hausdorff dimension of the image X(E) of a non-random Borel set \(E \subset [0,1]\), where X is a Lévy multistable process in \(\mathbf{R}.\) This extends the case where X is a classical stable Lévy process by letting the stability exponent \(\alpha \) be a smooth function. Hence, we are considering here non-homogeneous processes with increments which are not stationary and not necessarily independent. Contrary to the situation where the stability parameter is a constant, the dimension depends on the version of the multistable Lévy motion when the process has an infinite first moment.


Lévy processes Hausdorff dimension Multistable processes 

Mathematics Subject Classification

60K17 60K51 60K52 


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Authors and Affiliations

  1. 1.Univ Rennes, CNRS, IRMAR - UMR 6625RennesFrance

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