Darling--Erd\H{o}s theorem for L\'evy processes at zero

Peter Kevei; David Mason

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arXiv · 1906.06688

Darling--Erd\H{o}s theorem for L\'evy processes at zero

Peter Kevei·David Mason

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Abstract

We establish two equivalent versions of the Darling--Erd\H{o}s theorem for L\'evy processes in the domain of attraction of a stable process at zero with index $\alpha\in(0,2)$. In the course of our proof we obtain a number of maximal and exponential inequalities for general L\'evy processes, which should be of separate interest.

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Peter Kevei, David Mason. 2019-06-16. Darling--Erd\H{o}s theorem for L\'evy processes at zero. https://arxiv.org/abs/1906.06688

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