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 - http://www.scopus.com/inward/record.url?scp=85047370731&partnerID=8YFLogxK
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 -