On Functions Bounded by Karamata Functions

We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The r...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 237; no. 5; pp. 621 - 630
Main Authors Cadena, M., Kratz, M., Omey, E.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.03.2019
Springer
Springer Nature B.V
Subjects
Distribution functions
Laplace transforms
Mathematics
Mathematics and Statistics
Probability distributions
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Summary:We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The results are extended to functions that are bounded by O -regularly varying functions.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04187-z