Harmonizable fractional stable fields: Local nondeterminism and joint continuity of the local times

By applying a Fourier analytic argument, we prove that, for every α∈(0,2)α∈(0,2), the NN-parameter harmonizable fractional αα-stable field (HFααSF) is locally nondeterministic. When 0<α<10<α<1, this solves an open problem in Nolan (1989). Also, it allows us to establish the joint continuity of the local times of an (N,d)(N,d)-HFααSF for an arbitrary α∈(0,2)α∈(0,2), and to obtain new results concerning its sample paths.