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

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  • Ayache, Antoine
  • Xiao, Yimin

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.

Suggested Citation

  • Ayache, Antoine & Xiao, Yimin, 2016. "Harmonizable fractional stable fields: Local nondeterminism and joint continuity of the local times," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 171-185.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:171-185
    DOI: 10.1016/j.spa.2015.08.001
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    References listed on IDEAS

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    1. Biermé, Hermine & Lacaux, Céline, 2009. "Hölder regularity for operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2222-2248, July.
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