Limit theorem for maximum of the storage process with fractional Brownian motion as input

被引：30

作者：

Hüsler, J ^{[1
]}

Piterbarg, V ^{[1
]}

机构：

[1] Univ Bern, Dept Math & Stat, CH-3095 Bern, Switzerland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2004年 / 114卷 / 02期

关键词：

storage process; maximum; limit distribution; fractional Brownian motion; dense grid;

D O I：

10.1016/j.spa.2004.07.002

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：

The maximum M-T of the storage process Y(t) = sup(sgreater than or equal tot)(X(s) - X(t) - c(s - t)) in the interval [0, 7] is dealt with, in particular, for growing interval length T. Here X(s) is a fractional Brownian motion with Hurst parameter, 0<H<1. For fixed T the asymptotic behaviour Of MT was analysed by Piterbarg (Extremes 4(2) (2001) 147) by determining an approximation for the probability P{M-T > u} for u --> infinity. Using this expression the convergence P{M-T < u(T)(x)} --> G(x) as T --> infinity is derived where u(T)(x) --> infinity is a suitable normalization and G(x) = exp(-exp(-x)) the Gumbel distribution. Also the relation to the maximum of the process on a dense grid is analysed. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：231 / 250

页数：20