Extremes of threshold-dependent Gaussian processes
In this paper, we are concerned with the asymptotic behavior, as u → ∞ , of P { s u p t ∈ [ 0 , T ] X u ( 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 { s u p t ∈ [ 0 ,...
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| Veröffentlicht in: | Science China. Mathematics 2018-11, Vol.61 (11), p.1971-2002 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we are concerned with the asymptotic behavior, as
u
→
∞
, of
P
{
s
u
p
t
∈
[
0
,
T
]
X
u
(
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
{
s
u
p
t
∈
[
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. |
|---|---|
| ISSN: | 1674-7283 1869-1862 |
| DOI: | 10.1007/s11425-017-9225-7 |