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

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10.1007/s11009-016-9537-0

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Bai, L., Dȩbicki, K., Hashorva, E., & Luo, L. (2018). On Generalised Piterbarg Constants. Methodology and Computing in Applied Probability, 20(1), 137-164. https://doi.org/10.1007/s11009-016-9537-0

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On Generalised Piterbarg Constants

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