Wavelet series representation and geometric properties of harmonizable fractional stable sheets

Abstract

ABSTRACTLet be a real-valued N-parameter harmonizable fractional stable sheet with index . We establish a random wavelet series expansion for which is almost surely convergent in all the Hölder spaces , where M>0 and are arbitrary. One of the main ingredients for proving the latter result is the LePage representation for a rotationally invariant stable random measure. Also, let be an -valued harmonizable fractional stable sheet whose components are independent copies of . By making essential use of the regularity of its local times, we prove that, on an event of positive probability, the formula for the Hausdorff dimension of the inverse image holds for all Borel sets . This is referred to as a uniform Hausdorff dimension result for the inverse images.