Hausdorff dimension of operator semistable Lévy processes

Details Hausdorff dimension of operator semistable Lévy processes Hausdorff dimension of operator semistable Lévy processes

2012-04-26

arxiv.org/abs/1204.5897v1

Mathematics

Probability

23 pages

Scientific paper

Let $X=\{X(t)\}_{t\geq0}$ be an operator semistable L\'evy 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) L\'evy 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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