ABSTRACT
Let 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.
Acknowledgments
This work was finished during Yimin Xiao's visit to Université de Lille sponsored by CEMPI (ANR-11-LABX-0007-01). The hospitality from this university and the financial support from CEMPI are appreciated.
Disclosure statement
No potential conflict of interest was reported by the authors.