Extremes of threshold-dependent Gaussian processes

Long Bai; Krzysztof Dȩbicki; Enkelejd Hashorva; Lanpeng Ji

doi:10.1007/s11425-017-9225-7

Extremes of threshold-dependent Gaussian processes

Long Bai
, Krzysztof Dȩbicki^*
, Enkelejd Hashorva
, Lanpeng Ji

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

In this paper, we are concerned with the asymptotic behavior, as u→ ∞, of P{supt∈[0,T]Xu(t)>u}, where X_u(t) , t∈ [0 , T] , u> 0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns P{supt∈[0,T](X(t)+g(t))>u}, as u→ ∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.

Original language	English
Pages (from-to)	1971-2002
Number of pages	32
Journal	Science China Mathematics
Volume	61
Issue number	11
DOIs	https://doi.org/10.1007/s11425-017-9225-7
Publication status	Published - 1 Nov 2018
Externally published	Yes

Keywords

60G15
60G70
Gaussian processes
extremes
fractional Brownian motion
ruin probability
ruin time

Access to Document

10.1007/s11425-017-9225-7

Cite this

@article{e81b648a50ed4c81a5892592fba6f692,

title = "Extremes of threshold-dependent Gaussian processes",

abstract = "In this paper, we are concerned with the asymptotic behavior, as u→ ∞, of P\{supt∈[0,T]Xu(t)>u\}, where Xu(t) , t∈ [0 , T] , u> 0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns P\{supt∈[0,T](X(t)+g(t))>u\}, as u→ ∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.",

keywords = "60G15, 60G70, Gaussian processes, extremes, fractional Brownian motion, ruin probability, ruin time",

author = "Long Bai and Krzysztof Dȩbicki and Enkelejd Hashorva and Lanpeng Ji",

note = "Funding Information: Acknowledgements This work was supported by Swiss National Science Foundation (Grant No. 200021-166274) and the National Science Centre (Poland) (Grant No. 2015/17/B/ST1/01102) (2016–2019). The authors are thankful to the referees for several suggestions which have significantly improved their manuscript. Publisher Copyright: {\textcopyright} 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2018",

month = nov,

day = "1",

doi = "10.1007/s11425-017-9225-7",

language = "English",

volume = "61",

pages = "1971--2002",

journal = "Science China Mathematics",

issn = "1674-7283",

number = "11",

}

TY - JOUR

T1 - Extremes of threshold-dependent Gaussian processes

AU - Bai, Long

AU - Dȩbicki, Krzysztof

AU - Hashorva, Enkelejd

AU - Ji, Lanpeng

N1 - Funding Information: Acknowledgements This work was supported by Swiss National Science Foundation (Grant No. 200021-166274) and the National Science Centre (Poland) (Grant No. 2015/17/B/ST1/01102) (2016–2019). The authors are thankful to the referees for several suggestions which have significantly improved their manuscript. Publisher Copyright: © 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - In this paper, we are concerned with the asymptotic behavior, as u→ ∞, of P{supt∈[0,T]Xu(t)>u}, where Xu(t) , t∈ [0 , T] , u> 0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns P{supt∈[0,T](X(t)+g(t))>u}, as u→ ∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.

AB - In this paper, we are concerned with the asymptotic behavior, as u→ ∞, of P{supt∈[0,T]Xu(t)>u}, where Xu(t) , t∈ [0 , T] , u> 0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns P{supt∈[0,T](X(t)+g(t))>u}, as u→ ∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.

KW - 60G15

KW - 60G70

KW - Gaussian processes

KW - extremes

KW - fractional Brownian motion

KW - ruin probability

KW - ruin time

UR - https://www.scopus.com/pages/publications/85047370731

U2 - 10.1007/s11425-017-9225-7

DO - 10.1007/s11425-017-9225-7

M3 - Article

AN - SCOPUS:85047370731

SN - 1674-7283

VL - 61

SP - 1971

EP - 2002

JO - Science China Mathematics

JF - Science China Mathematics

IS - 11

ER -

Extremes of threshold-dependent Gaussian processes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this