{"ID":2895305,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09787","arxiv_id":"2507.09787","title":"Fixed-Point Estimation of the Drift Parameter in Stochastic Differential Equations Driven by Rough Multiplicative Fractional Noise","abstract":"We investigate the problem of estimating the drift parameter from $N$ independent copies of the solution of a stochastic differential equation driven by a multiplicative fractional Brownian noise with Hurst parameter $H\\in (1/3,1)$. Building on a least-squares-type object involving the Skorokhod integral, a key challenge consists in approximating this unobservable quantity with a computable fixed-point estimator, which requires addressing the correction induced by replacing the Skorokhod integral with its pathwise counterpart. To this end, a crucial technical contribution of this work is the reformulation of the Malliavin derivative of the process in a way that does not depend explicitly on the driving noise, enabling control of the approximation error in the multiplicative setting. For the case $H\\in (1/3,1/2]$, we further exploit results on two-dimensional Young integrals to manage the more intricate correction term that appears. As a result, we establish the well-posedness of a fixed-point estimator for any $H\\in (1/3,1)$, together with both an asymptotic confidence interval and a non-asymptotic risk bound. Finally, a numerical study illustrates the good practical performance of the proposed estimator.","short_abstract":"We investigate the problem of estimating the drift parameter from $N$ independent copies of the solution of a stochastic differential equation driven by a multiplicative fractional Brownian noise with Hurst parameter $H\\in (1/3,1)$. Building on a least-squares-type object involving the Skorokhod integral, a key challen...","url_abs":"https://arxiv.org/abs/2507.09787","url_pdf":"https://arxiv.org/pdf/2507.09787v2","authors":"[\"Chiara Amorino\",\"Laure Coutin\",\"Nicolas Marie\"]","published":"2025-07-13T20:57:40Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}