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
收藏
页码：147 / 159
页数：13
相关论文
共 50 条
  • [1] Limit theorem for maximum of the storage process with fractional Brownian motion as input
    Hüsler, J
    Piterbarg, V
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 114 (02) : 231 - 250
  • [2] Large Deviations of a Storage Process with Fractional Brownian Motion as Input
    Vladimir I. Piterbarg
    Extremes, 2001, 4 (2) : 147 - 164
  • [3] Convergence to the maximum process of a fractional Brownian motion with shot noise
    Wang, Yizao
    STATISTICS & PROBABILITY LETTERS, 2014, 90 : 33 - 41
  • [4] Approximation of Fractional Brownian Motion by Martingales
    Shklyar, Sergiy
    Shevchenko, Georgiy
    Mishura, Yuliya
    Doroshenko, Vadym
    Banna, Oksana
    METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2014, 16 (03) : 539 - 560
  • [5] Approximation of Fractional Brownian Motion by Martingales
    Sergiy Shklyar
    Georgiy Shevchenko
    Yuliya Mishura
    Vadym Doroshenko
    Oksana Banna
    Methodology and Computing in Applied Probability, 2014, 16 : 539 - 560
  • [6] On the maximum workload of a queue fed by fractional Brownian motion
    Zeevi, AJ
    Glynn, PW
    ANNALS OF APPLIED PROBABILITY, 2000, 10 (04): : 1084 - 1099
  • [7] Approximation of rough paths of fractional Brownian motion
    Millet, Annie
    Sanz-Sole, Marta
    SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS V, 2008, 59 : 275 - +
  • [8] On the supremum of γ-reflected processes with fractional Brownian motion as input
    Hashorva, Enkelejd
    Ji, Lanpeng
    Piterbarg, Vladimir I.
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (11) : 4111 - 4127
  • [9] Distribution of maximum loss of fractional Brownian motion with drift
    Caglar, Mine
    Vardar-Acar, Ceren
    STATISTICS & PROBABILITY LETTERS, 2013, 83 (12) : 2729 - 2734
  • [10] Small Values of the Maximum for the Integral of Fractional Brownian Motion
    G. Molchan
    A. Khokhlov
    Journal of Statistical Physics, 2004, 114 : 923 - 946
12345