Conditions for the finiteness of the moments of the volume of level sets
Resumen:
Let X(t) be a Gaussian random field R d → R. Using the notion of (d − 1)-integral geometric measures, we establish a relation between (a) the volume of level sets, and (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established.
| 2019 | |
|
Gaussian fields Nodal sets Crofton formula Kac-Rice formula |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/28107 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522785958821888 |
|---|---|
| author | Armentano, Diego |
| author2 | Azaïs, J.M. Ginsbourger, D. León, José Rafael |
| author2_role | author author author |
| author_facet | Armentano, Diego Azaïs, J.M. Ginsbourger, D. León, José Rafael |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Armentano Diego, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Azaïs J.M. Ginsbourger D. León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería |
| dc.creator.none.fl_str_mv | Armentano, Diego Azaïs, J.M. Ginsbourger, D. León, José Rafael |
| dc.date.accessioned.none.fl_str_mv | 2021-06-08T13:38:26Z |
| dc.date.available.none.fl_str_mv | 2021-06-08T13:38:26Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | Let X(t) be a Gaussian random field R d → R. Using the notion of (d − 1)-integral geometric measures, we establish a relation between (a) the volume of level sets, and (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established. |
| dc.format.extent.es.fl_str_mv | 8 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Armentano, D, Azaïs, J, Ginsbourger, D [y otro] "Conditions for the finiteness of the moments of the volume of level sets". Electronic Communications in Probability. [en línea] 2019, 24(17): 1-8. 8 h. DOI: 10.1214/19-ECP214 |
| dc.identifier.doi.none.fl_str_mv | 10.1214/19-ECP214 |
| dc.identifier.issn.none.fl_str_mv | 1083-589X |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/28107 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Bernoulli Society for Mathematical Statistics and Probability |
| dc.relation.ispartof.es.fl_str_mv | Electronic Communications in Probability, 2019, 24(17): 1-8 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.en.fl_str_mv | Gaussian fields Nodal sets Crofton formula Kac-Rice formula |
| dc.title.none.fl_str_mv | Conditions for the finiteness of the moments of the volume of level sets |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | Let X(t) be a Gaussian random field R d → R. Using the notion of (d − 1)-integral geometric measures, we establish a relation between (a) the volume of level sets, and (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_5ce5d3f626c6507b24d3bf1b1554aa84 |
| identifier_str_mv | Armentano, D, Azaïs, J, Ginsbourger, D [y otro] "Conditions for the finiteness of the moments of the volume of level sets". Electronic Communications in Probability. [en línea] 2019, 24(17): 1-8. 8 h. DOI: 10.1214/19-ECP214 1083-589X 10.1214/19-ECP214 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/28107 |
| publishDate | 2019 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| spelling | Armentano Diego, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Azaïs J.M.Ginsbourger D.León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería2021-06-08T13:38:26Z2021-06-08T13:38:26Z2019Armentano, D, Azaïs, J, Ginsbourger, D [y otro] "Conditions for the finiteness of the moments of the volume of level sets". Electronic Communications in Probability. [en línea] 2019, 24(17): 1-8. 8 h. DOI: 10.1214/19-ECP2141083-589Xhttps://hdl.handle.net/20.500.12008/2810710.1214/19-ECP214Let X(t) be a Gaussian random field R d → R. Using the notion of (d − 1)-integral geometric measures, we establish a relation between (a) the volume of level sets, and (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established.Submitted by Verdun Juan Pablo (jverdun@fcien.edu.uy) on 2021-06-03T14:23:59Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP214.pdf: 230298 bytes, checksum: 6707a689cd15026898b5da6919074854 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2021-06-08T12:50:29Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP214.pdf: 230298 bytes, checksum: 6707a689cd15026898b5da6919074854 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2021-06-08T13:38:26Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP214.pdf: 230298 bytes, checksum: 6707a689cd15026898b5da6919074854 (MD5) Previous issue date: 20198 h.application/pdfenengBernoulli Society for Mathematical Statistics and ProbabilityElectronic Communications in Probability, 2019, 24(17): 1-8Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)Gaussian fieldsNodal setsCrofton formulaKac-Rice formulaConditions for the finiteness of the moments of the volume of level setsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaArmentano, DiegoAzaïs, J.M.Ginsbourger, D.León, José RafaelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/28107/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/28107/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-838395http://localhost:8080/xmlui/bitstream/20.500.12008/28107/3/license_textd606c60c5d78967c4ed7a729e5bb402fMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Conditions for the finiteness of the moments of the volume of level sets Armentano, Diego Gaussian fields Nodal sets Crofton formula Kac-Rice formula |
| status_str | publishedVersion |
| title | Conditions for the finiteness of the moments of the volume of level sets |
| title_full | Conditions for the finiteness of the moments of the volume of level sets |
| title_fullStr | Conditions for the finiteness of the moments of the volume of level sets |
| title_full_unstemmed | Conditions for the finiteness of the moments of the volume of level sets |
| title_short | Conditions for the finiteness of the moments of the volume of level sets |
| title_sort | Conditions for the finiteness of the moments of the volume of level sets |
| topic | Gaussian fields Nodal sets Crofton formula Kac-Rice formula |
| url | https://hdl.handle.net/20.500.12008/28107 |
