Hausdorff dimension of the graph of an operator semistable Lévy process

Abstract

Let $X={X(t):t \geq 0}$ be an operator semistable Lévy process in $\mathbb{R}^d$ with exponent $E$, where $E$ is an invertible linear operator on $\mathbb{R}^d$. For an arbitrary Borel set $B \subseteq \mathbb{R}\_+$ we interpret the graph Gr$\_X(B)={(t,X(t)):t\ in B}$ as a semi-selfsimilar process on $\mathbb{R}^{d+1}$, whose distribution is not full, and calculate the Hausdorff dimension of Gr$\_X(B)$ in terms of the real parts of the eigenvalues of the exponent $E$ and the Hausdorff dimension of $B$.We use similar methods as applied in \[16] and \[8].