Harmonizable Fractional Stable Fields: Local Nondeterminism and Joint Continuity of the Local Times
نویسندگان
چکیده
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 [15]. 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. Running Title: Harmonizable Fractional Stable Fields: Local Nondeterminism and Local Times
منابع مشابه
Properties of Strong Local Nondeterminism and Local Times of Stable Random Fields
We establish properties of strong local nondeterminism for several classes of α-stable random fields such as harmonizable-type fractional stable fields with stationary increments, harmonizable and linear fractional stable sheets. We apply these properties to study existence and joint continuity of the local times of stable random fields. Mathematics Subject Classification (2000). 60G52; 60G17; ...
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