{"ID":2857352,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.09028","arxiv_id":"2510.09028","title":"Drift estimation for rough processes under small noise asymptotic : QMLE approach","abstract":"We consider a process $X^\\ve$ solution of a stochastic Volterra equation with an unknown parameter $θ^\\star$ in the drift function. The Volterra kernel is singular near zero, exhibiting a behavior comparable to $K\\_0(u)=cu^{α-1} \\id{u\u003e0}$ with $α\\in (1/2,1)$.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 inversion of the Volterra kernel. We show that this error decreases as $h^{1/2}$ regardless of the value of $α$. Then, we can introduce an explicit contrast function, which yields an efficient estimator when $\\ve \\to 0$.","short_abstract":"We consider a process $X^\\ve$ solution of a stochastic Volterra equation with an unknown parameter $θ^\\star$ in the drift function. The Volterra kernel is singular near zero, exhibiting a behavior comparable to $K\\_0(u)=cu^{α-1} \\id{u\u003e0}$ with $α\\in (1/2,1)$.It is assumed that the diffusion coefficient is proportional...","url_abs":"https://arxiv.org/abs/2510.09028","url_pdf":"https://arxiv.org/pdf/2510.09028v2","authors":"[\"Arnaud Gloter\",\"Nakahiro Yoshida\"]","published":"2025-10-10T05:59:08Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}