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Regularly log-periodic functions and some applications

Kevei Péter

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

159--182

We prove a Tauberian theorem for the Laplace-Stieltjes transform, a Karamata-type theorem, and a monotone density theorem in the framework of regularly log-periodic functions. We provide several applications of these results: for example, we prove that the tail of a nonnegative random variable is regularly log-periodic if and only if the same holds for its Laplace transform at 0, and we determine the exact tail behavior of fixed points of certain smoothing transforms.

A Tauberian Theorem for Weighted Means in Non-Archimedean Fields - Revisited and Revised

Natarajan P. N.

Commentationes Mathematicae

2014

Vol 54, No. 2

177--178

In this note, K denotes a complete, non-trivially valued, non-archimedean field. We correct a Tauberian theorem for weighted means in K proved earlier in [1].