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We consider the case where $f_\\theta\\PAR{x} \\sim_{x\\to 0} \\ABS{x}^{-\\al(\\theta)}L_\\theta(x)$ with $L_\\theta$ a slowly varying function and $\\al\\PAR{\\theta}\\in (-\\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^\\alpha_t,\\: \\alpha \\geq 1/2$ or ARFIMA processes."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.1077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-04T09:35:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"004bf4a9daae2accd53bc0ec68ad1c8b060267fc6f2c37f0246ac045759a5317","abstract_canon_sha256":"e8f9f69a9bd368b922b46ebe07b05aa29562aaa3ae025598e51b63d5374a9579"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.112440Z","signature_b64":"WQNZ+IxZ9ZjUE9SSltTwIhvwNn+D/E1nKbu45k8E/awKFubnhgfJU7WMT5eARcTulaTShIJsiFypHnODul6sCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97bdfe8da1fec339e78a6846024e5e182273016012ec7be77ebd5d14829a3ebb","last_reissued_at":"2026-05-18T03:12:58.111780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.111780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"LAN property for some fractional type Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"C\\'eline Lacaux (IECN), Fabrice Gamboa (IMT), Jean-Michel Loubes (IMT), Serge Cohen (IMT)","submitted_at":"2011-11-04T09:35:39Z","abstract_excerpt":"We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_\\theta$. 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