{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:46:56Z","timestamp":1762300016627},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T00:00:00Z","timestamp":1644796800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we employ a Gaussian-type heat kernel estimate to establish Krylov\u2019s estimate and Khasminskii\u2019s estimate for the Euler\u2013Maruyama (EM) algorithm. For applications, by taking Zvonkin\u2019s transformation into account, we investigate the convergence rate of the EM algorithm for a class of multidimensional stochastic differential equations (SDEs) with low regular drifts, which need not be piecewise Lipschitz.<\/jats:p>","DOI":"10.1017\/jpr.2021.56","type":"journal-article","created":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T09:41:58Z","timestamp":1644831718000},"page":"447-470","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["Convergence rate of the EM algorithm for SDEs with low regular drifts"],"prefix":"10.1017","volume":"59","author":[{"given":"Jianhai","family":"Bao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shao-Qin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,2,14]]},"reference":[{"key":"S0021900221000565_ref19","doi-asserted-by":"publisher","DOI":"10.1142\/p473"},{"key":"S0021900221000565_ref7","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901389530"},{"key":"S0021900221000565_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-021-01206-6"},{"key":"S0021900221000565_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2010.02.003"},{"key":"S0021900221000565_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2011.06.008"},{"key":"S0021900221000565_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1029867124"},{"key":"S0021900221000565_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/151004872"},{"key":"S0021900221000565_ref32","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v16-887"},{"key":"S0021900221000565_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.06.002"},{"key":"S0021900221000565_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2016.11.008"},{"key":"S0021900221000565_ref25","first-page":"1131","article-title":"Well-posedness of distribution dependent SDEs with singular drifts","volume":"27","author":"R\u00f6ckner","journal-title":"Bernoulli"},{"key":"S0021900221000565_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/19-AIHP997"},{"key":"S0021900221000565_ref27","volume-title":"Mathematics","author":"Shigekawa","year":"2004"},{"key":"S0021900221000565_ref10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2010.0348"},{"key":"S0021900221000565_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-018-0854-9"},{"key":"S0021900221000565_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"S0021900221000565_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-008-0164-1"},{"key":"S0021900221000565_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1262"},{"key":"S0021900221000565_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/PL00008735"},{"key":"S0021900221000565_ref34","doi-asserted-by":"publisher","DOI":"10.1070\/SM1974v022n01ABEH001689"},{"key":"S0021900221000565_ref30","doi-asserted-by":"publisher","DOI":"10.1214\/19-AIHP959"},{"key":"S0021900221000565_ref4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013764929351"},{"key":"S0021900221000565_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-004-0361-z"},{"key":"S0021900221000565_ref21","doi-asserted-by":"publisher","DOI":"10.1137\/18M1170017"},{"key":"S0021900221000565_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2018.12.012"},{"key":"S0021900221000565_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/11-AAP803"},{"key":"S0021900221000565_ref23","first-page":"1864","article-title":"On the Euler\u2013Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients","volume":"37","author":"Ngo","year":"2017","journal-title":"IMA J. 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