{"ID":6536396,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T08:33:44.272455028Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10230","arxiv_id":"2607.10230","title":"Nonparametric estimation of the diffusion coefficient of an ergodic diffusion process on non-compact supports under Osgood's conditions","abstract":"In this paper, we study the nonparametric estimation of the squared diffusion coefficient of an ergodic diffusion process on non-compact supports, when the two coefficients of the stochastic differential equation belong to a space larger than the space of Hölder continuous functions. The estimators are constructed by projection onto finite-dimensional spaces, thereby avoiding truncation of the dimension. We establish risk bounds of non-adaptive estimators and explicit rates of convergence for bounded and unbounded diffusion coefficients. A model selection procedure is performed, followed by the derivation of risk bounds using Talagrand's inequality. The theoretical results are completed with a numerical study over simulated data.","short_abstract":"In this paper, we study the nonparametric estimation of the squared diffusion coefficient of an ergodic diffusion process on non-compact supports, when the two coefficients of the stochastic differential equation belong to a space larger than the space of Hölder continuous functions. The estimators are constructed by p...","url_abs":"https://arxiv.org/abs/2607.10230","url_pdf":"https://arxiv.org/pdf/2607.10230v1","authors":"[\"Eddy-Michel Ella-Mintsa\"]","published":"2026-07-11T09:36:25Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}