Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A survey

Parthanil Roy ()
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Parthanil Roy: Indian Statistical Institute

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 4, 513-540

Abstract: Abstract This is a self-contained introduction to the applications of ergodic theory of nonsingular (also known as quasi-invariant) group actions and the structure theorem for finitely generated abelian groups on the extreme values of stationary symmetric stable random fields indexed by ℤ d . It is based on a mini course given in the http://www.isid.ac.in/ lps16/PastWebsites/LPS8/index.html Eighth Lectures on Probability and Stochastic Processes (held in the Bangalore Centre of Indian Statistical Institute during December 6–10, 2013) except that a few recent references have been added in the concluding part. This article is a survey of existing work and the proofs are therefore skipped or briefly outlined.

Keywords: Stable process; random field; extreme value theory; nonsingular group action; finitely generated abelian group (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0243-6

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