Generalized regular variation of second order
Generalized regular variation of second order
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DOI：
10.1017/s144678870000046x
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发表时间：
1996-12
期刊：
影响因子：
--
通讯作者：
L. Haan;U. Stadtmüller
中科院分区：
文献类型：
--
作者：
L. Haan;U. Stadtmüller
摘要 假设对于在$(0, +\infty)$上的一个可测函数$f$，存在一个正的辅助函数$a(t)$以及某个$\gamma \in \mathbb{R}$使得[此处应有相关条件，但原文缺失]。那么$f$被称为具有广义正则变化。为了控制极值理论中某些分布的估计量的渐近行为，我们需要研究二阶正则变化，也就是说，我们假设存在一个非平凡的极限，且带有第二个辅助函数$a_1(t)$。我们研究在这个极限关系（定义二阶广义正则变化）中可能的极限函数以及它们的吸引域。此外，对于具有所述性质的单调函数$f$的反函数，我们给出了相应的关系。最后，我们给出了一个将这些函数及其拉普拉斯变换相关联的阿贝尔 - 陶伯定理。
Abstract Assume that for a measurable funcion f on (0, ∞) there exist a positive auxiliary function a(t) and some γ ∈ R such that . Then f is said to be of generalized regular variation. In order to control the asymptotic behaviour of certain estimators for distributions in extreme value theory we are led to study regular variation of second order, that is, we assume that exists non-trivially with a second auxiliary function a1(t). We study the possible limit functions in this limit relation (defining generalized regular variation of second order) and their domains of attraction. Furthermore we give the corresponding relation for the inverse function of a monotone f with the stated property. Finally, we present an Abel-Tauber theorem relating these functions and their Laplace transforms.