On Generalised Piterbarg Constants

被引：20

作者：

Bai, Long ^{[1
]}

Debicki, Krzysztof ^{[2
]}

Hashorva, Enkelejd ^{[1
]}

Luo, Li ^{[1
]}

机构：

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

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

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2018年 / 20卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Pickands constants; Piterbarg constants; Gaussian process; Extremes; Exact asymptotics; Brown-Resnick stationarity; GAUSSIAN-PROCESSES; EXTREMES; BOUNDS;

D O I：

10.1007/s11009-016-9537-0

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 investigate generalised Piterbarg constants P-alpha,delta(h) = lim(T -> infinity) E {sup(t is an element of delta Z boolean AND[0,T]) e(root 2B alpha(t)-vertical bar t vertical bar alpha-h(t))} determined in terms of a fractional Brownian motion B-alpha with Hurst index alpha/2 is an element of(0, 1], the non-negative constant delta and alpha continuous function h. We show that these constants, similarly to generalised Pickands constants, appear naturally in the tail asymptotic behaviour of supremum of Gaussian processes. Further, we derive several bounds for P-alpha, delta(h) and in special cases explicit formulas are obtained.

引用

页码：137 / 164

页数：28

共 36 条

[1]

Adler Robert J, 2007, RANDOM FIELDS GEOMET, V80

[2] ON EXTREMAL THEORY FOR STATIONARY-PROCESSES [J].

ALBIN, JMP .

ANNALS OF PROBABILITY, 1990, 18 (01) :92-128

[3]

Berman S. M., 1992, The Wadsworth & Brooks/Cole Statistics/Probability Series

[4] SOJOURNS AND EXTREMES OF STATIONARY-PROCESSES [J].

BERMAN, SM .

ANNALS OF PROBABILITY, 1982, 10 (01) :1-46

[5]

Burnecki K., 2002, PROB MATH STAT, V22, P193

[6] Excursion probabilities of isotropic and locally isotropic Gaussian random fields on manifolds [J].

Cheng, Dan .

EXTREMES, 2017, 20 (02) :475-487

[7] Distribution of the height of local maxima of Gaussian random fields [J].

Cheng, Dan ;

Schwartzman, Armin .

EXTREMES, 2015, 18 (02) :213-240

[8]

[Debicki K. Debicki K.], 2005, [Теория вероятностей и ее применения, Theory of Probability and its Applications, Teoriya veroyatnostei i ee primeneniya], V50, P396

[9] Simulation of the asymptotic constant in some fluid models [J].

Debicki, K ;

Michna, Z ;

Rolski, T .

STOCHASTIC MODELS, 2003, 19 (03) :407-423

[10] Exact overflow asymptotics for queues with many Gaussian inputs [J].

Debicki, K ;

Mandjes, M .

JOURNAL OF APPLIED PROBABILITY, 2003, 40 (03) :704-720

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