Extremes of vector-valued Gaussian processes with Trend

被引：6

作者：

Bai, Long ^{[1
]}

Debicki, Krzysztof ^{[2
]}

Liu, Peng ^{[1
]}

机构：

[1] Univ Lausanne, Dept Actuarial Sci, UNIL Dorigny, CH-1015 Lausanne, Switzerland

[2] Univ Wroclaw, Math Inst, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 465卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Vector-valued Gaussian process; Extremes; Conjunction; Piterbarg constant; Pickands constant; FRACTIONAL BROWNIAN-MOTION; RUIN PROBLEM; CONSTANTS; QUADRANT; SUPREMUM; FIELDS;

D O I：

10.1016/j.jmaa.2018.04.069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X(t) (X-1(t),..., X-n (t)), t is an element of T subset of IR be a centered vector-valued Gaussian process with independent components and continuous trajectories, and h(t) = h(1)(t), ..., h(n)(t)), t is an element of T be a vector -valued continuous function. We investigate the asymptotics of P{sup(t is an element of T) min(1 <= i <= n) (X-i(t) + h(i)(t)) > u} as u -> infinity. As an illustration to the derived results we analyze two important classes of X(t): with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：47 / 74

页数：28