The Hausdorff dimension of the range of the Lévy multistable processes

R. Guével ()
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R. Guével: Univ Rennes, CNRS, IRMAR - UMR 6625

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 765-780

Abstract: Abstract We compute the Hausdorff dimension of the image X(E) of a non-random Borel set $$E \subset [0,1]$$ E ⊂ [ 0 , 1 ] , where X is a Lévy multistable process in $$\mathbf{R}.$$ R . This extends the case where X is a classical stable Lévy process by letting the stability exponent $$\alpha $$ α 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.

Keywords: Lévy processes; Hausdorff dimension; Multistable processes; 60K17; 60K51; 60K52 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0847-8

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