On convolution closure properties of subexponentiality approaching from densities

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 giv...

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Bibliographic Details
Main Authors Matsui, Muneya, Watanabe, Toshiro
Format Journal Article
LanguageEnglish
Published 31.08.2023
Subjects
Mathematics - Probability
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Summary: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.
DOI:10.48550/arxiv.2308.16727