The Hausdorff Dimension of Operator Semistable Lévy Processes

摘要

Let X = {X(t)}_(t≥0) be an operator semistable Lévy process in R~d with exponent E, where E is an invertible linear operator on R~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) Lévy process, for an arbitrary Borel set B ? R_+ 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.