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Large deviations for point processes based on stationary sequences with heavy tails
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
2010 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 1, 1-40 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we propose a framework that facilitates the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track both of the magnitude of the extreme values of a process and the order in which these extreme values appear. Particular emphasis is put on (infinite) linear processes with random coefficients. The proposed framework provides a fairly complete description of the joint asymptotic behavior of the large values of the stationary sequence. We apply the general result on large deviations for point processes to derive the asymptotic decay of certain probabilities related to partial sum processes as well as ruin probabilities.

Place, publisher, year, edition, pages
2010. Vol. 47, no 1, 1-40 p.
Keyword [en]
Stationary sequence, regular variation, large deviations, point process
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-28310DOI: 10.1239/jap/1269610814ISI: 000276521700001Scopus ID: 2-s2.0-80053930658OAI: oai:DiVA.org:kth-28310DiVA: diva2:386679
Funder
Swedish Research Council
Note
QC 20110113Available from: 2011-01-13 Created: 2011-01-12 Last updated: 2017-12-11Bibliographically approved

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Hult, Henrik

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