Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform

Zhaolei Cui, Yuebao Wang () and Hui Xu
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Zhaolei Cui: School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou 215000, China
Yuebao Wang: School of Mathematical Sciences, Soochow University, Suzhou 215006, China
Hui Xu: School of Mathematical Sciences, Soochow University, Suzhou 215006, China

Mathematics, 2022, vol. 10, issue 21, 1-24

Abstract: In this paper, we show that the local distribution class L l o c ∩ OS l o c 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 L l o c ∩ OS l o c , 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.

Keywords: infinitely divisible distribution roots; Lévy distribution; local distribution class; random convolution roots; closure; Esscher transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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