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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Ayache, Antoine¹  Xiao, Yimin² 

[1] Univ Lille 1, CNRS, UMR 8524, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

关键词: Harmonizable fractional stable field;    Local nondeterrninism;    Local times;    Joint continuity;    Holder condition;    Hausdorff dimension;   

DOI  :  10.1016/j.spa.2015.08.001

来源: Elsevier

【 摘 要 】

By applying a Fourier analytic argument, we prove that, for every alpha is an element of (0, 2), the N-parameter harmonizable fractional a-stable field (HF alpha SF) is locally nondeterministic. When 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)-HF alpha SF for an arbitrary alpha is an element of(0, 2), and to obtain new results concerning its sample paths. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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