{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:15:05Z","timestamp":1753884905491,"version":"3.41.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,12,29]],"date-time":"2021-12-29T00:00:00Z","timestamp":1640736000000},"content-version":"vor","delay-in-days":362,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSP-2021\/162"],"award-info":[{"award-number":["RSP-2021\/162"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We consider statistical experiments associated with a L\u00e9vy process  observed along a deterministic scheme (<jats:italic>i<\/jats:italic><jats:italic>u<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, \u20091 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>). We assume that under a probability \u2119<jats:sub><jats:italic>\u03b8<\/jats:italic><\/jats:sub>, the r.v. <jats:italic>X<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>, \u2009<jats:italic>t<\/jats:italic> &gt; 0, has a probability density function &gt;<jats:italic>o<\/jats:italic>, which is regular enough relative to a parameter <jats:italic>\u03b8<\/jats:italic> \u2208 (0, <jats:italic>\u221e<\/jats:italic>). We prove that the sequence of the associated statistical models has the LAN property at each <jats:italic>\u03b8<\/jats:italic>, and we investigate the case when <jats:italic>X<\/jats:italic> is the product of an unknown parameter <jats:italic>\u03b8<\/jats:italic> by another L\u00e9vy process <jats:italic>Y<\/jats:italic> with known characteristics. We illustrate the last results by the case where <jats:italic>Y<\/jats:italic> is attracted by a stable process.<\/jats:p>","DOI":"10.1155\/2021\/3143324","type":"journal-article","created":{"date-parts":[[2021,12,29]],"date-time":"2021-12-29T22:06:40Z","timestamp":1640815600000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Local Asymptotic Normality Complexity Arising in a Parametric Statistical L\u00e9vy Model"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3153-3948","authenticated-orcid":false,"given":"Wissem","family":"Jedidi","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,12,29]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0197-7"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4946-7"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345464"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01194919"},{"key":"e_1_2_9_5_2","first-page":"193","article-title":"Estimation of the diffusion coefficient for diffusion processes: random sampling","volume":"21","author":"Genon-Catalot V.","year":"1994","journal-title":"Scandinavian Journal of Statistics"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2015.01.002"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001190"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.14490\/jjss.39.49"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2010.12.011"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1051\/ps\/2011101"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2008.00858.x"},{"key":"e_1_2_9_12_2","unstructured":"RammehH. LPMA CNRS-UMR 7599 1994 University of Paris Paris France PhD thesis."},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02514-7"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/s0040585x97983286"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02619-9"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/065"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/s0040585x97983419"},{"key":"e_1_2_9_18_2","unstructured":"FarH. LPMA CNRS-UMR 7599 University of Paris Paris France PhD thesis."},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1515\/9783110850826"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(89)90053-7"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1051\/ps:1997114"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0246-0203(97)80120-3"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/3143324.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/3143324.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/3143324","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:21:38Z","timestamp":1723242098000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/3143324"}},"subtitle":[],"editor":[{"given":"Ning","family":"Cai","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/3143324"],"URL":"https:\/\/doi.org\/10.1155\/2021\/3143324","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-08-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-11-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-12-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"3143324"}}