On Generalised Piterbarg Constants

Long Bai; Krzysztof Dȩbicki; Enkelejd Hashorva; Li Luo

doi:10.1007/s11009-016-9537-0

On Generalised Piterbarg Constants

Long Bai, Krzysztof Dȩbicki, Enkelejd Hashorva^*, Li Luo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We investigate generalised Piterbarg constants (Formula presented.) determined in terms of a fractional Brownian motion B_α with Hurst index α/2∈(0,1], the non-negative constant δ and a 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_α,δ^h and in special cases explicit formulas are obtained.

Original language	English
Pages (from-to)	137-164
Number of pages	28
Journal	Methodology and Computing in Applied Probability
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s11009-016-9537-0
Publication status	Published - 1 Mar 2018
Externally published	Yes

Keywords

Brown-Resnick stationarity
Exact asymptotics
Extremes
Gaussian process
Pickands constants
Piterbarg constants

Access to Document

10.1007/s11009-016-9537-0

Cite this

@article{b354ac0ad4ca4ca4bf05db584dcdc4df,

title = "On Generalised Piterbarg Constants",

abstract = "We investigate generalised Piterbarg constants (Formula presented.) determined in terms of a fractional Brownian motion Bα with Hurst index α/2∈(0,1], the non-negative constant δ and a 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 Pα,δh and in special cases explicit formulas are obtained.",

keywords = "Brown-Resnick stationarity, Exact asymptotics, Extremes, Gaussian process, Pickands constants, Piterbarg constants",

author = "Long Bai and Krzysztof Dȩbicki and Enkelejd Hashorva and Li Luo",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2018",

month = mar,

day = "1",

doi = "10.1007/s11009-016-9537-0",

language = "English",

volume = "20",

pages = "137--164",

journal = "Methodology and Computing in Applied Probability",

issn = "1387-5841",

number = "1",

}

TY - JOUR

T1 - On Generalised Piterbarg Constants

AU - Bai, Long

AU - Dȩbicki, Krzysztof

AU - Hashorva, Enkelejd

AU - Luo, Li

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We investigate generalised Piterbarg constants (Formula presented.) determined in terms of a fractional Brownian motion Bα with Hurst index α/2∈(0,1], the non-negative constant δ and a 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 Pα,δh and in special cases explicit formulas are obtained.

AB - We investigate generalised Piterbarg constants (Formula presented.) determined in terms of a fractional Brownian motion Bα with Hurst index α/2∈(0,1], the non-negative constant δ and a 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 Pα,δh and in special cases explicit formulas are obtained.

KW - Brown-Resnick stationarity

KW - Exact asymptotics

KW - Extremes

KW - Gaussian process

KW - Pickands constants

KW - Piterbarg constants

UR - http://www.scopus.com/inward/record.url?scp=85008477711&partnerID=8YFLogxK

U2 - 10.1007/s11009-016-9537-0

DO - 10.1007/s11009-016-9537-0

M3 - Article

AN - SCOPUS:85008477711

SN - 1387-5841

VL - 20

SP - 137

EP - 164

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 1

ER -

On Generalised Piterbarg Constants

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this