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When the drift is H\u00f6lder continuous, we show that the limiting law of the rescaled fluctuations around the true solution is characterised as the unique solution of a hybrid Young\u2013It\u00f4 differential equation. When the drift is bounded and has positive Sobolev regularity, this limit is characterised by the solution of a transformed SDE. Our results are extensions of the results of Jacod\u2013Kurtz\u2013Protter (1991, 1998) in which SDEs with differentiable coefficients were considered. To compensate for the lack of regularity of the drifts, we utilise the regularisation effect from the non-degenerate noise.<\/jats:p>","DOI":"10.1007\/s40072-026-00411-5","type":"journal-article","created":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T17:03:26Z","timestamp":1775495006000},"page":"2175-2212","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A central limit theorem for the Euler method for SDEs with irregular drifts"],"prefix":"10.1007","volume":"14","author":[{"given":"Konstantinos","family":"Dareiotis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M\u00e1t\u00e9","family":"Gerencs\u00e9r","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Khoa","family":"L\u00ea","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,6]]},"reference":[{"issue":"4","key":"411_CR1","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1007\/s00440-021-01080-2","volume":"181","author":"O Butkovsky","year":"2021","unstructured":"Butkovsky, O., Dareiotis, K., Gerencs\u00e9r, M.: Approximation of SDEs: a stochastic sewing approach. 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