We introduce different types of multivariate regularly varying functions and define a new class of positive and measurable functions that are bounded between such multivariate Karamata functions. We study integrals and Laplace transforms of these functions. We use the results to study the tail of convolutions of bivariate distribution functions.
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.
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Cadena, M., Omey, E. Functions Bounded by Karamata Functions in ℝD. J Math Sci 246, 460–475 (2020). https://doi.org/10.1007/s10958-020-04752-x
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DOI: https://doi.org/10.1007/s10958-020-04752-x