Multiple points of operator semistable Lévy processes

Abstract

We determine the Hausdorff dimension of $k$-multiple points for a symmetric operator semistable Lévy process $X=\{X(t),t\in {\mathbb{R}}_{+}\}$ in terms of the eigenvalues of its stability exponent. We also give a necessary and sufficient condition for the existence of $k$-multiple points. Our results extend to all $k\ge 2$ the recent work [23], where the set of double points $(k=2)$ was studied in the symmetric operator stable case.

24 pages, editorial changes, to appear in J. Theoret. Probab