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

Antoine Ayache and Yimin Xiao

Stochastic Processes and their Applications, 2016, vol. 126, issue 1, 171-185

Abstract: By applying a Fourier analytic argument, we prove that, for every α∈(0,2), the N-parameter harmonizable fractional α-stable field (HFαSF) is locally nondeterministic. When 0<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)-HFαSF for an arbitrary α∈(0,2), and to obtain new results concerning its sample paths.

Keywords: Harmonizable fractional stable field; Local nondeterminism; Local times; Joint continuity; Hölder condition; Hausdorff dimension (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.08.001

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