Approximation of the maximum of storage process with fractional Brownian motion as input

被引：1

作者：

Xu, Zhengchun ^{[1
]}

Tan, Zhongquan ^{[1
]}

Tang, Linjun ^{[1
]}

机构：

[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 140卷

基金：

中国博士后科学基金; 美国国家科学基金会;

关键词：

Extreme values; Storage process; Fractional Brownian motion; Discrete time process; MAX-DISCRETIZATION THEOREM; STATIONARY-PROCESSES; CONTINUOUS-TIME; EXTREMES; GRIDS;

D O I：

10.1016/j.spl.2018.05.015

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, the asymptotic relation between the maximum of the storage process and the maximum of the process sampled at discrete time points is studied. It is shown that these two maxima are asymptotically independent or dependent when the grids of the discrete time points are sufficiently sparse or the so-called Pickands grids. The results complete a gap in Husler and Piterbarg (2004) which showed that the two maxima are asymptotically coincident when the grids of the discrete time points are sufficiently dense. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：147 / 159

页数：13

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