Stable random fields, point processes and large deviations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Fasen, Vicky¹  Roy, Parthanil² 

[1] Karlsruhe Inst Technol, Inst Stochast, D-76133 Karlsruhe, Germany

[2] Indian Stat Inst, Stat & Math Unit, Kolkata 700108, India

关键词: Large deviations;    Point processes;    Stable processes;    Random fields;    Extreme value theory;    Nonsingular group actions;   

DOI  :  10.1016/j.spa.2015.09.020

来源: Elsevier

【 摘 要 】

We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric alpha-stable (0 < alpha < 2) discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic theoretic and group theoretic structures of the underlying nonsingular group action, we observe different large deviation behaviours of this point process sequence. We use our results to study the large deviations of various functionals (e.g., partial sum, maxima, etc.) of stationary symmetric stable fields. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free