强次指数分布在卷积下的非闭包性

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Modelling and Control Pub Date : 2022-12-23 DOI:10.15388/namc.2023.28.30208

D. Konstantinides, R. Leipus, J. Šiaulys

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引用次数: 0

摘要

本文研究一类强次指数分布的卷积闭包问题，记为S*。首先，我们证明，如果F, G∈L，那么对于所有(某些)p∈(0)，F*G, FG和pF + (1 - p)G的包含;1)进入类S*是等效的。然后，使用kl ppelberg和Villasenor[卷积等价分布的卷积闭包问题的完整解，J. Math]构造的例子。分析的达成。[j]，我们证明了S*在卷积下是不闭合的。

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On the non-closure under convolution for strong subexponential distributions

In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.