| dc.contributor.author | Döbler, Christian | |
| dc.contributor.author | Kasprzak, Mikołaj | |
| dc.contributor.author | Peccati, Giovanni | |
| dc.date.accessioned | 2022-10-19T12:48:42Z | |
| dc.date.available | 2022-10-19T12:48:42Z | |
| dc.date.issued | 2022-02-22 | |
| dc.identifier.uri | https://hdl.handle.net/1721.1/145898 | |
| dc.description.abstract | Abstract
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
$$t=1$$
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). | en_US |
| dc.publisher | Springer Berlin Heidelberg | en_US |
| dc.relation.isversionof | https://doi.org/10.1007/s00440-022-01114-3 | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.source | Springer Berlin Heidelberg | en_US |
| dc.title | The multivariate functional de Jong CLT | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Döbler, Christian, Kasprzak, Mikołaj and Peccati, Giovanni. 2022. "The multivariate functional de Jong CLT." | |
| dc.contributor.department | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems | |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2022-10-19T03:20:45Z | |
| dc.language.rfc3066 | en | |
| dc.rights.holder | The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature | |
| dspace.embargo.terms | Y | |
| dspace.date.submission | 2022-10-19T03:20:45Z | |
| mit.license | PUBLISHER_POLICY | |
| mit.metadata.status | Authority Work and Publication Information Needed | en_US |
