Stable random fields, point processes and large deviations

Vicky Fasen and Parthanil Roy

Stochastic Processes and their Applications, 2016, vol. 126, issue 3, 832-856

Abstract: We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric α-stable (0<α<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.

Keywords: Large deviations; Point processes; Stable processes; Random fields; Extreme value theory; Nonsingular group actions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:3:p:832-856

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DOI: 10.1016/j.spa.2015.09.020

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