Extremes of a certain class of Gaussian processes

被引：106

作者：

Hüsler, J

Piterbarg, V

机构：

[1] Univ Bern, Inst Stat Math, CH-3012 Bern, Switzerland

[2] Moscow State Univ, Moscow, Russia

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1999年 / 83卷 / 02期

关键词：

extreme values; Gaussian processes; fractional Brownian motions; self-similar processes;

D O I：

10.1016/S0304-4149(99)00041-1

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：

We consider the extreme values of fractional Brownian motions, self-similar Gaussian processes and more general Gaussian processes which have a trend -ct(beta) for some constants c, beta > 0 and a variance t(2H). We derive the tail behaviour of these extremes and show that they occur mainly in the neighbourhood of the unique point lo where the related boundary function (u + ct(beta))/t(H) is minimal. We consider the case that H < beta. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：257 / 271

页数：15