The multivariate functional de Jong CLT
We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants i...
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| Veröffentlicht in: | Probability theory and related fields 2022-10, Vol.184 (1-2), p.367-399 |
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| container_title | Probability theory and related fields |
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| creator | Döbler, Christian Kasprzak, Mikołaj Peccati, Giovanni |
| description | We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in
t
=
1
vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947–1985, 2010). |
| doi_str_mv | 10.1007/s00440-022-01114-3 |
| format | Article |
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t
=
1
vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947–1985, 2010).</description><identifier>ISSN: 0178-8051</identifier><identifier>EISSN: 1432-2064</identifier><identifier>DOI: 10.1007/s00440-022-01114-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Economics ; Finance ; Insurance ; Management ; Mathematical and Computational Biology ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Multivariate analysis ; Operations Research/Decision Theory ; Probability ; Probability Theory and Stochastic Processes ; Quantitative Finance ; Random variables ; Statistics ; Statistics for Business ; Theorems ; Theoretical</subject><ispartof>Probability theory and related fields, 2022-10, Vol.184 (1-2), p.367-399</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-6d9106d09a5d86a4a072e398e7d6c040d4198d409426ac4df6596a03402667263</citedby><cites>FETCH-LOGICAL-c319t-6d9106d09a5d86a4a072e398e7d6c040d4198d409426ac4df6596a03402667263</cites><orcidid>0000-0003-2631-2072</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00440-022-01114-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00440-022-01114-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Döbler, Christian</creatorcontrib><creatorcontrib>Kasprzak, Mikołaj</creatorcontrib><creatorcontrib>Peccati, Giovanni</creatorcontrib><title>The multivariate functional de Jong CLT</title><title>Probability theory and related fields</title><addtitle>Probab. Theory Relat. Fields</addtitle><description>We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in
t
=
1
vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. 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t
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| source | Business Source Complete; Springer Nature - Complete Springer Journals |
| subjects | Economics Finance Insurance Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Multivariate analysis Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Quantitative Finance Random variables Statistics Statistics for Business Theorems Theoretical |
| title | The multivariate functional de Jong CLT |
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