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

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• 作者：Antoine Ayache^a ; ^{Antoine.Ayache@math.univ-lille1.fr" class="auth_mail" title="E-mail the corresponding author} ; ; Yimin Xiao^b ; ^{xiao@stt.msu.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：60G52 ; 60G17 ; 60G18 ; 60G60
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：126
• 期：1
• 页码：171-185
• 全文大小：254 K

文摘

By applying a Fourier analytic argument, we prove that, for every α∈(0,2)$\alpha \in (0,2)$, the N$N$-parameter harmonizable fractional α$\alpha$-stable field (HFα$\alpha$SF) is locally nondeterministic. When 0<α<1$0<\alpha <1$, 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)$(N,d)$-HFα$\alpha$SF for an arbitrary α∈(0,2)$\alpha \in (0,2)$, and to obtain new results concerning its sample paths.