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We then extend the methodology to discrete observations, showing that the same convergence rates can be attained. Moreover, we establish concentration inequalities for the estimator and introduce a data-driven bandwidth selection procedure that adapts to unknown smoothness. Numerical experiments for the fractional Ornstein\u2013Uhlenbeck process illustrate the estimator\u2019s practical performance. Finally, our results weaken the usual convexity assumptions on the drift component, allowing us to consider settings where strong convexity only holds outside a compact set.<\/jats:p>","DOI":"10.1214\/26-aos2637","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T12:49:03Z","timestamp":1790945343000},"page":"2286-2324","source":"Crossref","is-referenced-by-count":0,"title":["Fast convergence rates for estimating the stationary density in SDEs driven by a fractional Brownian motion with semicontractive drift"],"prefix":"10.1214","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2467-1445","authenticated-orcid":false,"given":"Chiara","family":"Amorino","sequence":"first","affiliation":[{"name":"Universitat Pompeu Fabra and Barcelona School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eulalia","family":"Nualart","sequence":"additional","affiliation":[{"name":"Universitat Pompeu Fabra and Barcelona School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabien","family":"Panloup","sequence":"additional","affiliation":[{"name":"Universit\u00e9 d\u2019Angers, CNRS, LAREMA, SFR Mathstic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julian","family":"Sieber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London & G-Research, 1 Soho Place, London W1D 3BG"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"32","doi-asserted-by":"publisher","unstructured":"<small>Istas, J.<\/small> and <small>Lang, G.<\/small> (1997). 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