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 |
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| container_end_page | 2002 |
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| container_issue | 11 |
| container_start_page | 1971 |
| container_title | Science China. Mathematics |
| container_volume | 61 |
| creator | Bai, Long Dȩbicki, Krzysztof Hashorva, Enkelejd Ji, Lanpeng |
| description | 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. |
| doi_str_mv | 10.1007/s11425-017-9225-7 |
| format | Article |
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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.</description><identifier>ISSN: 1674-7283</identifier><identifier>EISSN: 1869-1862</identifier><identifier>DOI: 10.1007/s11425-017-9225-7</identifier><language>eng</language><publisher>Beijing: Science China Press</publisher><subject>Applications of Mathematics ; Asymptotic properties ; Brownian motion ; Gaussian process ; Mathematics ; Mathematics and Statistics</subject><ispartof>Science China. Mathematics, 2018-11, Vol.61 (11), p.1971-2002</ispartof><rights>Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-f1ac8b45636a6c0b6794c628a626949122db86a728f7281f35eb76d10b878d3</citedby><cites>FETCH-LOGICAL-c359t-f1ac8b45636a6c0b6794c628a626949122db86a728f7281f35eb76d10b878d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11425-017-9225-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11425-017-9225-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Bai, Long</creatorcontrib><creatorcontrib>Dȩbicki, Krzysztof</creatorcontrib><creatorcontrib>Hashorva, Enkelejd</creatorcontrib><creatorcontrib>Ji, Lanpeng</creatorcontrib><title>Extremes of threshold-dependent Gaussian processes</title><title>Science China. Mathematics</title><addtitle>Sci. China Math</addtitle><description>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.</description><subject>Applications of Mathematics</subject><subject>Asymptotic properties</subject><subject>Brownian motion</subject><subject>Gaussian process</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1674-7283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1UE1Lw0AQXUTBUvsDvAU8r-7MJvtxlFKrUPCg92WTbGxLm8SdBPTfuyGCJ2eYj8N7b4bH2C2IexBCPxBAjgUXoLnFtOgLtgCjLE8NL9OudM41GnnNVkRHkUJakWu5YLj5GmI4B8q6Jhv2MdC-O9W8Dn1o69AO2daPRAffZn3sqkAU6IZdNf5EYfU7l-ztafO-fua71-3L-nHHK1nYgTfgK1PmhZLKq0qUStu8Umi8QmVzC4h1aZRPbzWpoJFFKLWqQZRGm1ou2d2smu5-joEGd-zG2KaDDgEFypQ6oWBGVbEjiqFxfTycffx2INzkjZu9cckbN3njJg7OHErY9iPEP-X_ST_3lWT9</recordid><startdate>20181101</startdate><enddate>20181101</enddate><creator>Bai, Long</creator><creator>Dȩbicki, Krzysztof</creator><creator>Hashorva, Enkelejd</creator><creator>Ji, Lanpeng</creator><general>Science China Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20181101</creationdate><title>Extremes of threshold-dependent Gaussian processes</title><author>Bai, Long ; Dȩbicki, Krzysztof ; Hashorva, Enkelejd ; Ji, Lanpeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-f1ac8b45636a6c0b6794c628a626949122db86a728f7281f35eb76d10b878d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applications of Mathematics</topic><topic>Asymptotic properties</topic><topic>Brownian motion</topic><topic>Gaussian process</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bai, Long</creatorcontrib><creatorcontrib>Dȩbicki, Krzysztof</creatorcontrib><creatorcontrib>Hashorva, Enkelejd</creatorcontrib><creatorcontrib>Ji, Lanpeng</creatorcontrib><collection>CrossRef</collection><jtitle>Science China. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bai, Long</au><au>Dȩbicki, Krzysztof</au><au>Hashorva, Enkelejd</au><au>Ji, Lanpeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extremes of threshold-dependent Gaussian processes</atitle><jtitle>Science China. Mathematics</jtitle><stitle>Sci. China Math</stitle><date>2018-11-01</date><risdate>2018</risdate><volume>61</volume><issue>11</issue><spage>1971</spage><epage>2002</epage><pages>1971-2002</pages><issn>1674-7283</issn><eissn>1869-1862</eissn><abstract>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.</abstract><cop>Beijing</cop><pub>Science China Press</pub><doi>10.1007/s11425-017-9225-7</doi><tpages>32</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1674-7283 |
| ispartof | Science China. Mathematics, 2018-11, Vol.61 (11), p.1971-2002 |
| issn | 1674-7283 1869-1862 |
| language | eng |
| recordid | cdi_proquest_journals_2120232327 |
| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Asymptotic properties Brownian motion Gaussian process Mathematics Mathematics and Statistics |
| title | Extremes of threshold-dependent Gaussian processes |
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