Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics

• Published in: Extremes (Boston) Vol. 27; no. 4; pp. 613 - 641
• Main Authors: Dȩbicki, Krzysztof, Ji, Lanpeng, Novikov, Svyatoslav
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-12-2024; Springer Nature B.V
• Subjects: Brownian motion; Civil Engineering; Economics; Environmental Management; Finance; Hydrogeology; Insurance; Management; Mathematics and Statistics; Neighborhoods; Quality Control; Reliability; Safety and Risk; Statistics; Statistics for Business; Dimension reduction; Extremes; Secondary—60G70; Quadratic programming problem; Primary—60G15; Exact asymptotics; Multi-dimensional fractional Brownian motion; Large deviations
• ISSN: 1386-1999; 1572-915X
• DOI: 10.1007/s10687-024-00489-x

For
{
B
H
(
t
)
=
(
B
H
,
1
(
t
)
,
…
,
B
H
,
d
(
t
)
)
⊤
,
t
≥
0
}
, where
{
B
H
,
i
(
t
)
,
t
≥
0
}
,
1
≤
i
≤
d
are mutually independent fractional Brownian motions, we obtain the exact asymptotics of
P
(
∃
t
≥
0
:
A
B
H
(
t
)
-
μ
t
>
ν
u
)
,
u
→
∞
,
where
A
is a non-singular
d
×
d
matrix and
μ
=
(
μ
1
,
…
,
μ
d
)
⊤
∈
R
d
,
ν
=
(
ν
1
,
…
,
ν
d
)
⊤
∈
R
d
are such that there exists some
1
≤
i
≤
d
such that
μ
i
>
0
,
ν
i
>
0
.