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• W4308439076 abstract "In this paper, we show that the local distribution class Lloc∩OSloc is not closed under infinitely divisible distribution roots, i.e., there is an infinitely divisible distribution which belongs to the class, while the corresponding Lévy distribution does not. Conversely, we give a condition, under which, if an infinitely divisible distribution belongs to the class Lloc∩OSloc, then so does the Lévy distribution. Furthermore, we find some sufficient conditions that are more concise and intuitive. Using different methods, we also give a corresponding result for another local distribution class, which is larger than the above class. To prove the above results, we study the local closure under random convolution roots. In particular, we obtain a result on the local closure under the convolution root. In these studies, the Esscher transform of distribution plays a key role, which clarifies the relationship between these local distribution classes and related global distribution classes." @default.
• W4308439076 created "2022-11-11" @default.
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• W4308439076 date "2022-11-05" @default.
• W4308439076 modified "2023-10-18" @default.
• W4308439076 title "Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform" @default.
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• W4308439076 doi "https://doi.org/10.3390/math10214128" @default.
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