论文标题
无限分布的密度的亚指数
Subexponentialiy of densities of infinitely divisible distributions
论文作者
论文摘要
我们显示了三个特性的无限分布分布的等效性：密度的次指数性，其lévy度量密度的次指数性以及在Lévy测量密度上的单调型假设下，密度与其Lévy度量密度之间的密度与Lévy度量密度之间的尾部等效性。关键的假设是，Lévy度量密度的尾巴是渐近函数或最终是非进攻的。我们的条件是新颖的，涵盖了相当广泛的无限分布分布。已经得出了分析密度下指数的几种重要特性，例如[卷积，卷积根和渐近等效性的闭合特性]和分解特性。此外，我们说明结果适用于开发绝对连续的无限分配分布的统计推断。
We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its Lévy measure and the tail equivalence between the density and its Lévy measure density, under monotonic-type assumptions on the Lévy measure density. The key assumption is that tail of the Lévy measure density is asymptotic to a non-increasing function or is eventually non-increasing. Our conditions are novel and cover a rather wide class of infinitely divisible distributions. Several significant properties for analyzing the subexponentiality of densities have been derived such as closure properties of [ convolution, convolution roots and asymptotic equivalence ] and the factorization property. Moreover, we illustrate that the results are applicable for developing the statistical inference of subexponential infinitely divisible distributions which are absolutely continuous.
