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

被引：0

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：

美国国家科学基金会; 中国博士后科学基金;

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

共 50 条

[1] Limit theorem for maximum of the storage process with fractional Brownian motion as input
Hüsler, J
Piterbarg, V
[J]. 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
[J]. Extremes, 2001, 4 (2) : 147 - 164
[3] On the maximum of a fractional Brownian motion
Molchan, GM
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1999, 44 (01) : 97 - 102
[4] Convergence to the maximum process of a fractional Brownian motion with shot noise
Wang, Yizao
[J]. STATISTICS & PROBABILITY LETTERS, 2014, 90 : 33 - 41
[5] Distribution of the maximum of a fractional Brownian motion
Sinai, YG
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1997, 52 (02) : 359 - 378
[6] Approximation of Fractional Brownian Motion by Martingales
Shklyar, Sergiy
Shevchenko, Georgiy
Mishura, Yuliya
Doroshenko, Vadym
Banna, Oksana
[J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2014, 16 (03) : 539 - 560
[7] Approximation of Fractional Brownian Motion by Martingales
Sergiy Shklyar
Georgiy Shevchenko
Yuliya Mishura
Vadym Doroshenko
Oksana Banna
[J]. Methodology and Computing in Applied Probability, 2014, 16 : 539 - 560
[8] Binomial approximation of Brownian motion and its maximum
Carbone, R
[J]. STATISTICS & PROBABILITY LETTERS, 2004, 69 (03) : 271 - 285
[9] Perturbative expansion for the maximum of fractional Brownian motion
Delorme, Mathieu
Wiese, Kay Joerg
[J]. PHYSICAL REVIEW E, 2016, 94 (01)
[10] APPROXIMATION OF FRACTIONAL BROWNIAN MOTION BY THE VERNIERS INTEGRAL
Mishura, Y. S.
Banna, O. L.
[J]. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2008, 79 : 96 - 104

← 1 2 3 4 5 →