Hausdorff dimension of operator semistable Lévy processes

Peter Kern; Lina Wedrich

doi:10.1007/s10959-012-0422-7

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arXiv · 1204.5897

Hausdorff dimension of operator semistable Lévy processes

Peter Kern·Lina Wedrich

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Abstract

Let $X=\{X(t)\}_{t\geq0}$ be an operator semistable Lévy process in $\rd$ with exponent $E$, where $E$ is an invertible linear operator on $\rd$ and $X$ is semi-selfsimilar with respect to $E$. By refining arguments given in Meerschaert and Xiao \cite{MX} for the special case of an operator stable (selfsimilar) Lévy process, for an arbitrary Borel set $B\subseteq\rr_+$ we determine the Hausdorff dimension of the partial range $X(B)$ in terms of the real parts of the eigenvalues of $E$ and the Hausdorff dimension of $B$.

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BibTeX RIS

Peter Kern, Lina Wedrich. 2012-04-26. Hausdorff dimension of operator semistable Lévy processes. https://doi.org/10.1007/s10959-012-0422-7

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