2023/08/31 by Muneya Matsui, Toshiro Watanabe, Matsui, Muneya +1
Mathematics · Physics and Astronomy · #60E05 #60G70 #62F10 #Applied mathematics #Artificial intelligence #Closure (psychology) #Computer science #Convolution (computer science) #Counterexample #Discrete mathematics #FOS: Mathematics #Geometry #Law #Mathematical and Theoretical Analysis #Mathematics #Probability (math.PR) #Product (mathematics) #Pure mathematics #Quantum Mechanics and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2308.16727
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.