Hausdorff dimension of the graph of an operator semistable L\'evy process

Abstract

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