Maximal moments and uniform modulus of continuity for stable random fields

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:136

Article

Panigrahi, Snigdha¹  Roy, Parthanil²  Xiao, Yimin³ 

[1] Univ Michigan, Dept Stat, Ann Arbor, MI 48109 USA

[2] Indian Stat Inst, Theoret Stat & Math Unit, Bangalore 560059, Karnataka, India

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

关键词: Random field;    Stable process;    Uniform modulus of continuity;    Extreme value theory;    Nonsingular group actions;   

DOI  :  10.1016/j.spa.2021.02.002

来源: Elsevier

【 摘 要 】

In this work, we provide sharp bounds on the rate of growth of maximal moments for stationary symmetric stable random fields when the underlying nonsingular group action (or its restriction to a suitable lower rank subgroup) has a nontrivial dissipative component. We also investigate the relationship between this rate of growth and the path regularity properties of self-similar stable random fields with stationary increments, and establish uniform modulus of continuity of such fields. In the process, a new notion of weak effective dimension is introduced for stable random fields and is connected to maximal moments and path properties. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free