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Regularly log-periodic functions and some applications. (English) Zbl 1460.44001

The author proves a Tauberian theorem for the Laplace-Stieltjes transform, and Karamata-type theorems in the framework of regularly log-periodic functions. After some preliminaries, first he deals with a Tauberian theorem for the Laplace-Stieltjes transform and then proves the direct half of the Karamata theorem, and a monotone density theorem. Further, it is proved that the tail of a nonnegative random variable is regularly log-periodic if and only if the same is true for its Laplace transform at 0, and the exact tail behavior of fixed points of a certain smoothing transform is obtained.

MSC:

44A10 Laplace transform
40E05 Tauberian theorems
60E99 Distribution theory
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