The Hausdorff Dimension of Operator Semistable Levy Processes

Let X={X(t)} (ta parts per thousand yen0) be an operator semistable L,vy process in a"e (d) with exponent E, where E is an invertible linear operator on a"e (d) and X is semi-selfsimilar with respect to E. By refining arguments given in Meerschaert and Xiao (Stoch. Process. Appl. 115, 55-75, 2005) for the special case of an operator stable (selfsimilar) L,vy process, for an arbitrary Borel set BaS dagger a"e(+) 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.