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Extremal behavior of stochastic integrals driven by regularly varying Levy processes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2007 (English)In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 35, no 1, 309-339 p.Article in journal (Refereed) Published
Abstract [en]

We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.

Place, publisher, year, edition, pages
2007. Vol. 35, no 1, 309-339 p.
Keyword [en]
regular variation, extreme values, stochastic integrals, Levy processes, limit-theorems
Identifiers
URN: urn:nbn:se:kth:diva-16513DOI: 10.1214/009117906000000548ISI: 000245415500010Scopus ID: 2-s2.0-38649118753OAI: oai:DiVA.org:kth-16513DiVA: diva2:334555
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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