On the finiteness of the moments of the measure of level sets of random fields
Resumen:
General conditions on smooth real valued random fields are given that ensure the finiteness of the moments of the measure of their level sets. As a by product a new generalized Kac-Rice formula (KRF) for the expectation of the measure of these level sets is obtained when the second moment can be uniformly bounded. The conditions involve (i) the differentiability of the trajectories up to a certain order k, (ii) the finiteness of the moments of the k-th partial derivatives of the field up to another order, (iii) the boundedness of the joint density of the field and some of its derivatives. Particular attention is given to the shot noise processes and fields. Other applications include stationary Gaussian processes, Chi-square processes and regularized diffusion processes.
| 2020 | |
| MATHEMATICS - PROBABILITY | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44752 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522809958629376 |
|---|---|
| author | Armentano, Diego |
| author2 | Azaïs, Jean Marc Dalmao Artigas, Federico León, José Rafael Mordecki, Ernesto |
| author2_role | author author author author |
| author_facet | Armentano, Diego Azaïs, Jean Marc Dalmao Artigas, Federico León, José Rafael Mordecki, Ernesto |
| 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 Económicas y de Administracón. Azaïs Jean Marc Dalmao Artigas Federico, Universidad de la República (Uruguay). CENUR León José Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Armentano, Diego Azaïs, Jean Marc Dalmao Artigas, Federico León, José Rafael Mordecki, Ernesto |
| dc.date.accessioned.none.fl_str_mv | 2024-07-15T12:17:54Z |
| dc.date.available.none.fl_str_mv | 2024-07-15T12:17:54Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.none.fl_txt_mv | General conditions on smooth real valued random fields are given that ensure the finiteness of the moments of the measure of their level sets. As a by product a new generalized Kac-Rice formula (KRF) for the expectation of the measure of these level sets is obtained when the second moment can be uniformly bounded. The conditions involve (i) the differentiability of the trajectories up to a certain order k, (ii) the finiteness of the moments of the k-th partial derivatives of the field up to another order, (iii) the boundedness of the joint density of the field and some of its derivatives. Particular attention is given to the shot noise processes and fields. Other applications include stationary Gaussian processes, Chi-square processes and regularized diffusion processes. |
| dc.description.es.fl_txt_mv | Versión permitida preprint Publicado también en: Brazilian Journal of Probability and Statistics, 2023, 37(1): 219-245. DOI: 10.1214/23-BJPS568 |
| dc.format.extent.es.fl_str_mv | 19 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Armanetano, D, Azaïs, J, Dalmao Artigas, y otros. "On the finiteness of the moments of the measure of level sets of random fields"[Preprint]. Publicado en: Mathematics (Probability). 2020 arXiv:1909.10243v2, ago 2020, pp 1-19. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.1909.10243 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44752 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Probability), arXiv:1909.10243v2, ago 2020, pp 1-19 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 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.other.es.fl_str_mv | MATHEMATICS - PROBABILITY |
| dc.title.none.fl_str_mv | On the finiteness of the moments of the measure of level sets of random fields |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Versión permitida preprint |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_1a4fce3f9ae774e57d4c65bf34922aa3 |
| identifier_str_mv | Armanetano, D, Azaïs, J, Dalmao Artigas, y otros. "On the finiteness of the moments of the measure of level sets of random fields"[Preprint]. Publicado en: Mathematics (Probability). 2020 arXiv:1909.10243v2, ago 2020, pp 1-19. 10.48550/arXiv.1909.10243 |
| 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:20.500.12008/44752 |
| publishDate | 2020 |
| 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Armentano Diego, Universidad de la República (Uruguay). Facultad de Ciencias Económicas y de Administracón.Azaïs Jean MarcDalmao Artigas Federico, Universidad de la República (Uruguay). CENURLeón José Rafael, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2024-07-15T12:17:54Z2024-07-15T12:17:54Z2020Armanetano, D, Azaïs, J, Dalmao Artigas, y otros. "On the finiteness of the moments of the measure of level sets of random fields"[Preprint]. Publicado en: Mathematics (Probability). 2020 arXiv:1909.10243v2, ago 2020, pp 1-19.https://hdl.handle.net/20.500.12008/4475210.48550/arXiv.1909.10243Versión permitida preprintPublicado también en: Brazilian Journal of Probability and Statistics, 2023, 37(1): 219-245. DOI: 10.1214/23-BJPS568General conditions on smooth real valued random fields are given that ensure the finiteness of the moments of the measure of their level sets. As a by product a new generalized Kac-Rice formula (KRF) for the expectation of the measure of these level sets is obtained when the second moment can be uniformly bounded. The conditions involve (i) the differentiability of the trajectories up to a certain order k, (ii) the finiteness of the moments of the k-th partial derivatives of the field up to another order, (iii) the boundedness of the joint density of the field and some of its derivatives. Particular attention is given to the shot noise processes and fields. Other applications include stationary Gaussian processes, Chi-square processes and regularized diffusion processes.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-11T19:13:02Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 1909.10243v2.pdf: 288181 bytes, checksum: 2f64b247b353a55c6933228700b2f88a (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-15T12:06:36Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 1909.10243v2.pdf: 288181 bytes, checksum: 2f64b247b353a55c6933228700b2f88a (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-15T12:17:54Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 1909.10243v2.pdf: 288181 bytes, checksum: 2f64b247b353a55c6933228700b2f88a (MD5) Previous issue date: 202019 h.application/pdfenengarXivMathematics (Probability), arXiv:1909.10243v2, ago 2020, pp 1-19Las 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)MATHEMATICS - PROBABILITYOn the finiteness of the moments of the measure of level sets of random fieldsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaArmentano, DiegoAzaïs, Jean MarcDalmao Artigas, FedericoLeón, José RafaelMordecki, ErnestoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44752/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44752/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | On the finiteness of the moments of the measure of level sets of random fields Armentano, Diego MATHEMATICS - PROBABILITY |
| status_str | submittedVersion |
| title | On the finiteness of the moments of the measure of level sets of random fields |
| title_full | On the finiteness of the moments of the measure of level sets of random fields |
| title_fullStr | On the finiteness of the moments of the measure of level sets of random fields |
| title_full_unstemmed | On the finiteness of the moments of the measure of level sets of random fields |
| title_short | On the finiteness of the moments of the measure of level sets of random fields |
| title_sort | On the finiteness of the moments of the measure of level sets of random fields |
| topic | MATHEMATICS - PROBABILITY |
| url | https://hdl.handle.net/20.500.12008/44752 |
