On convolution closure properties of subexponentiality approaching from densities

Muneya Matsui; Toshiro Watanabe

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arXiv · 2308.16727

On convolution closure properties of subexponentiality approaching from densities

Muneya Matsui·Toshiro Watanabe

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Abstract

Non-closedness of subexponentiality by the convolution operation is well-known. We go a step further and show that subexponentiality and non-subexponentiality are generally changeable by the convolution. We also give several conditions, by which (non-) subexponentiality is kept. Most results are given with densities, which are easily converted to those for distributions. As a by-product, we give counterexamples to several past results, which were used to derive the non-closedness of the convolution, and modify the original proof.

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Muneya Matsui, Toshiro Watanabe. 2023-08-31. On convolution closure properties of subexponentiality approaching from densities. https://arxiv.org/abs/2308.16727

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