Hausdorff dimension of operator semistable Lévy processes

Abstract

Let $X=\{X(t){\}}_{t\ge 0}$ 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 $B$.

23 pages

References in corpus (1)

• Levy processes: Capacity and Hausdorff dimension

Cited by in corpus (3)

• Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties
• On exact Hausdorff measure functions of operator semistable Lévy processes
• The dimension of the St. Petersburg game