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Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings
Let W = { W n : n ∈ N } be a sequence of random vectors in R d , d ≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of W , that is, for any vector q > 0 in R d , we find that log P (there exists n ∈ N : W n u q ) as u → ∞. We follow the approach of the restricted large d...
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| Published in: | Journal of applied probability 2015-03, Vol.52 (1), p.68-81 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3 |
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| cites | cdi_FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3 |
| container_end_page | 81 |
| container_issue | 1 |
| container_start_page | 68 |
| container_title | Journal of applied probability |
| container_volume | 52 |
| creator | Kosiński, K. M. Mandjes, M. |
| description | Let
W
= {
W
n
:
n
∈
N
} be a sequence of random vectors in
R
d
,
d
≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of
W
, that is, for any vector
q
> 0 in
R
d
, we find that log
P
(there exists
n
∈
N
:
W
n
u
q
) as
u
→ ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every
q
≥
0
, and some scalings {
a
n
}, {
v
n
}, (1 /
v
n
)log
P
(
W
n
/
a
n
≥
u
q
) has a, continuous in
q
, limit
J
W
(
q
). We allow the scalings {
a
n
} and {
v
n
} to be regularly varying with a positive index. This approach is general enough to incorporate sequences
W
, such that the probability law of
W
n
/
a
n
satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature. |
| doi_str_mv | 10.1017/S0021900200012201 |
| format | article |
| fullrecord | <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_1017_S0021900200012201</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1017_S0021900200012201</sourcerecordid><originalsourceid>FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3</originalsourceid><addsrcrecordid>eNplUMFOwzAUixBIlMEHcMsPFN5LmqQ9TtOASWMcNs5VmqQjqG2mpEjs72kFNy62JVuWbELuER4QUD3uARhWEwAAMgZ4QTIslMglKHZJstnOZ_-a3KT0OYUKUamM7LbhqKMfP3pv6DKd-9MYRm8SbUOkr1_d6K3v3ZB8GHRH199jdL1L9H2wLtJdGDo_OB3p3uhJHdMtuWp1l9zdHy_I4Wl9WL3k27fnzWq5zU0FmAsFWjYlQyuZwMLZhjPJK4nKOKeNaQpoZaVlyUWrywK0abhV0xJ0YIR1fEHwt9bEkFJ0bX2KvtfxXCPU8x_1vz_4D6WlU6E</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings</title><source>JSTOR Archival Journals</source><creator>Kosiński, K. M. ; Mandjes, M.</creator><creatorcontrib>Kosiński, K. M. ; Mandjes, M.</creatorcontrib><description>Let
W
= {
W
n
:
n
∈
N
} be a sequence of random vectors in
R
d
,
d
≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of
W
, that is, for any vector
q
> 0 in
R
d
, we find that log
P
(there exists
n
∈
N
:
W
n
u
q
) as
u
→ ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every
q
≥
0
, and some scalings {
a
n
}, {
v
n
}, (1 /
v
n
)log
P
(
W
n
/
a
n
≥
u
q
) has a, continuous in
q
, limit
J
W
(
q
). We allow the scalings {
a
n
} and {
v
n
} to be regularly varying with a positive index. This approach is general enough to incorporate sequences
W
, such that the probability law of
W
n
/
a
n
satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.1017/S0021900200012201</identifier><language>eng</language><ispartof>Journal of applied probability, 2015-03, Vol.52 (1), p.68-81</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3</citedby><cites>FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kosiński, K. M.</creatorcontrib><creatorcontrib>Mandjes, M.</creatorcontrib><title>Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings</title><title>Journal of applied probability</title><description>Let
W
= {
W
n
:
n
∈
N
} be a sequence of random vectors in
R
d
,
d
≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of
W
, that is, for any vector
q
> 0 in
R
d
, we find that log
P
(there exists
n
∈
N
:
W
n
u
q
) as
u
→ ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every
q
≥
0
, and some scalings {
a
n
}, {
v
n
}, (1 /
v
n
)log
P
(
W
n
/
a
n
≥
u
q
) has a, continuous in
q
, limit
J
W
(
q
). We allow the scalings {
a
n
} and {
v
n
} to be regularly varying with a positive index. This approach is general enough to incorporate sequences
W
, such that the probability law of
W
n
/
a
n
satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.</description><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNplUMFOwzAUixBIlMEHcMsPFN5LmqQ9TtOASWMcNs5VmqQjqG2mpEjs72kFNy62JVuWbELuER4QUD3uARhWEwAAMgZ4QTIslMglKHZJstnOZ_-a3KT0OYUKUamM7LbhqKMfP3pv6DKd-9MYRm8SbUOkr1_d6K3v3ZB8GHRH199jdL1L9H2wLtJdGDo_OB3p3uhJHdMtuWp1l9zdHy_I4Wl9WL3k27fnzWq5zU0FmAsFWjYlQyuZwMLZhjPJK4nKOKeNaQpoZaVlyUWrywK0abhV0xJ0YIR1fEHwt9bEkFJ0bX2KvtfxXCPU8x_1vz_4D6WlU6E</recordid><startdate>201503</startdate><enddate>201503</enddate><creator>Kosiński, K. M.</creator><creator>Mandjes, M.</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201503</creationdate><title>Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings</title><author>Kosiński, K. M. ; Mandjes, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c901-570a6b821d62514edb32639617ceeaccb40f69a6835fa840acb3d76071e0c5de3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kosiński, K. M.</creatorcontrib><creatorcontrib>Mandjes, M.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kosiński, K. M.</au><au>Mandjes, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings</atitle><jtitle>Journal of applied probability</jtitle><date>2015-03</date><risdate>2015</risdate><volume>52</volume><issue>1</issue><spage>68</spage><epage>81</epage><pages>68-81</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><abstract>Let
W
= {
W
n
:
n
∈
N
} be a sequence of random vectors in
R
d
,
d
≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of
W
, that is, for any vector
q
> 0 in
R
d
, we find that log
P
(there exists
n
∈
N
:
W
n
u
q
) as
u
→ ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every
q
≥
0
, and some scalings {
a
n
}, {
v
n
}, (1 /
v
n
)log
P
(
W
n
/
a
n
≥
u
q
) has a, continuous in
q
, limit
J
W
(
q
). We allow the scalings {
a
n
} and {
v
n
} to be regularly varying with a positive index. This approach is general enough to incorporate sequences
W
, such that the probability law of
W
n
/
a
n
satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.</abstract><doi>10.1017/S0021900200012201</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 2015-03, Vol.52 (1), p.68-81 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_1017_S0021900200012201 |
| source | JSTOR Archival Journals |
| title | Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings |
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