Stable Random Fields, Point Processes and Large Deviations
Probability
2014-10-21 v1
Abstract
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian 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.
Cite
@article{arxiv.1410.5398,
title = {Stable Random Fields, Point Processes and Large Deviations},
author = {Vicky Fasen and Parthanil Roy},
journal= {arXiv preprint arXiv:1410.5398},
year = {2014}
}