Local subexponentiality and infinitely divisible distributions

Muneya Matsui; Toshiro Watanabe

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arXiv · 2302.07487

Local subexponentiality and infinitely divisible distributions

Muneya Matsui·Toshiro Watanabe

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Abstract

We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible distributions is characterized with new conditions, and local subexponentiality is newly characterized in the two-sided case. In the process closedness properties of these subexponentialities are derived, particularly for distributions on $\R$. Most results are obtained by exploiting monotonic-type assumptions. We apply our results to distributions of supremum of a random work and a randomly stopped iid sum.

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Muneya Matsui, Toshiro Watanabe. 2023-02-15. Local subexponentiality and infinitely divisible distributions. https://arxiv.org/abs/2302.07487

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