{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:40:25Z","timestamp":1776840025320,"version":"3.51.2"},"reference-count":49,"publisher":"American Mathematical Society (AMS)","issue":"354","license":[{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071488"],"award-info":[{"award-number":["12071488"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371417"],"award-info":[{"award-number":["12371417"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971488"],"award-info":[{"award-number":["11971488"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we study the strong approximation of scalar stochastic differential equations (SDEs), which take values in a domain and have non-Lipschitz coefficients. By combining a Lamperti-type transformation with a semi-implicit discretization approach and a taming strategy, we construct a domain-preserving scheme that strongly converges under weak assumptions. Moreover, we show that this scheme has strong convergence order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1.5\">\n                        <mml:semantics>\n                          <mml:mn>1.5<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">1.5<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    under additional assumptions on the coefficients of the SDE. In our scheme, the domain preservation is a consequence of the semi-implicit discretization approach, while the taming strategy allows controlling terms of the scheme that admit singularities but are required to obtain the desired order.\n                  <\/p>\n                  <p>Our general convergence results are applied to various SDEs from applications, with sub-linearly or super-linearly growing and non-globally Lipschitz coefficients. Numerical experiments are presented to illustrate our theoretical findings.<\/p>","DOI":"10.1090\/mcom\/4014","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T11:17:13Z","timestamp":1725535033000},"page":"1815-1862","source":"Crossref","is-referenced-by-count":1,"title":["A strong order 1.5 boundary preserving discretization scheme for scalar SDEs defined in a domain"],"prefix":"10.1090","volume":"94","author":[{"given":"Ruishu","family":"Liu","sequence":"first","affiliation":[]},{"given":"Andreas","family":"Neuenkirch","sequence":"additional","affiliation":[]},{"given":"Xiaojie","family":"Wang","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1016\/j.spl.2012.10.034","article-title":"Strong order one convergence of a drift implicit Euler scheme: application to the CIR process","volume":"83","author":"Alfonsi, Aur\u00e9lien","year":"2013","journal-title":"Statist. 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