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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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 237; no. 5; pp. 621 - 630 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
04.03.2019
Springer Springer Nature B.V |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Audience | Academic |
| Author | Omey, E. Cadena, M. Kratz, M. |
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| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2019 COPYRIGHT 2019 Springer Copyright Springer Nature B.V. 2019 |
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| References | KaramataJSur un mode de croissance r´eguli`ere des fonctionsMathematica (Cluj)19304385356.0907.01 CadenaMKratzMOmeyEOn the order of functions at infinityJ. Math. Anal. Appl.20174521109125362801010.1016/j.jmaa.2017.02.0421379.26004 OmeyEOn the difference between the product and the convolution product of distribution functionsPubl. Inst. Math. B´eograd, N.S.1994556911114513249810824.60032 M. Cadena, Contributions to the Study of Extreme Behavior and Applications, Doctoral Thesis, Université Pierre et Marie Curie, Paris, France (2016). CadenaMKratzMNew results for tails of probability distributions according to their asymptotic decayStat. Probab. Let.2016109178183343497510.1016/j.spl.2015.10.0181329.60084 BinghamNGoldieCTeugelsJRegular Variation1989EnglandCambridge University Press0667.26003 GelukJLde HaanLRegular Variation, Extensions and Tauberian Theorems1987AmsterdamCWI Tract 400624.26003 de HaanLOn Regular Variation and its Applications to the Weak Convergence of Sample Extremes1970AmsterdamMathematical Centre Tracts 320226.60039 M Cadena (4187_CR3) 2016; 109 4187_CR2 M Cadena (4187_CR4) 2017; 452 J Karamata (4187_CR7) 1930; 4 L Haan de (4187_CR6) 1970 E Omey (4187_CR8) 1994; 55 N Bingham (4187_CR1) 1989 JL Geluk (4187_CR5) 1987 |
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| SubjectTerms | Distribution functions Laplace transforms Mathematics Mathematics and Statistics Probability distributions |
| Title | On Functions Bounded by Karamata Functions |
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