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Theory of Probability and Mathematical Statistics

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A generalization of Karamata's theorem on the asymptotic behavior of integrals


Authors: V. V. Buldygin and V. V. Pavlenkov
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 15-26
MSC (2010): Primary 26A12, 26A48; Secondary 34C41
DOI: https://doi.org/10.1090/S0094-9000-2010-00806-4
Published electronically: January 14, 2011
MathSciNet review: 2667306
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Abstract: A generalization of Karamata's theorem on the asymptotic behavior of integrals of regularly varying functions with components is obtained in the paper.


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Additional Information

V. V. Buldygin
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (“KPI”), Peremogy Avenue 37, Kyiv 03056, Ukraine
Email: matan@ntu-kpi.kiev.ua

V. V. Pavlenkov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (“KPI”), Peremogy Avenue 37, Kyiv 03056, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-2010-00806-4
Keywords: Regularly varying functions, Karamata’s theorem, asymptotic behavior of integrals, oscillating functions
Received by editor(s): November 3, 2009
Published electronically: January 14, 2011
Article copyright: © Copyright 2010 American Mathematical Society

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