{"paper":{"title":"Drift estimation for rough processes under small noise asymptotic : QMLE approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arnaud Gloter (LaMME), nakahiro yoshida","submitted_at":"2025-10-10T05:59:08Z","abstract_excerpt":"We consider a process $X^\\ve$ solution of a stochastic Volterra equation with an unknown parameter $\\theta^\\star$ in the drift function. The Volterra kernel is singular near zero, exhibiting a behavior comparable to $K\\_0(u)=cu^{\\alpha-1} \\id{u>0}$ with $\\alpha \\in (1/2,1)$.It is assumed that the diffusion coefficient is proportional to $\\ve \\to 0$. Based on discrete observations, with a mesh size $h\\to0$, of the Volterra process, we construct a Quasi Maximum Likelihood Estimator. The main step is to assess the error arising in the reconstruction of the path of a semimartingale from the invers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.09028","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.09028/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}