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Regularly varying probability densities. (English) Zbl 1164.26302

The authors prove that the convolution of regularly varying probability densities is asymptotically equivalent to their sum. Various extensions of this result are given, concerning densities with tails which are rapidly varying, O-regularly varying, almost decreasing, of bounded decrease. Cases involving subexponentiality remain open.

MSC:

26A12 Rate of growth of functions, orders of infinity, slowly varying functions
60E05 Probability distributions: general theory
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