{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:35:02Z","timestamp":1768408502696,"version":"3.49.0"},"reference-count":4,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,9,1]],"date-time":"2013-09-01T00:00:00Z","timestamp":1377993600000},"content-version":"unspecified","delay-in-days":243,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>In the original article [<jats:italic>LMS J.\u00a0Comput. Math.<\/jats:italic> 15 (2012) 71\u201383], the authors use a discrete form of the It\u00f4 formula, developed by Appleby, Berkolaiko and Rodkina [<jats:italic>Stochastics<\/jats:italic> 81 (2009) no. 2, 99\u2013127], to show that the almost sure asymptotic stability of a particular two-dimensional test system is preserved when\u00a0the discretisation step size is small. In this Corrigendum, we identify an implicit assumption in the\u00a0original proof of the discrete It\u00f4 formula that, left unaddressed, would preclude its application to the test system of interest. We resolve this problem by reproving the relevant part of the discrete It\u00f4 formula in such a way that confirms its applicability to our test equation. Thus, we reaffirm the main results and conclusions of the original article.<\/jats:p>","DOI":"10.1112\/s146115701300017x","type":"journal-article","created":{"date-parts":[[2013,10,7]],"date-time":"2013-10-07T10:12:32Z","timestamp":1381140752000},"page":"366-372","source":"Crossref","is-referenced-by-count":3,"title":["Corrigendum: On the use of a discrete form of the It\u00f4 formula in the article \u2018Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising\u00a0stochastic\u00a0perturbations\u2019"],"prefix":"10.1112","volume":"16","author":[{"given":"Gregory","family":"Berkolaiko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evelyn","family":"Buckwar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C\u00f3nall","family":"Kelly","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandra","family":"Rodkina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2013,9,1]]},"reference":[{"key":"S146115701300017X_r3","doi-asserted-by":"publisher","DOI":"10.1137\/090771843"},{"key":"S146115701300017X_r1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/17442500802088541","article-title":"Non-exponential stability and decay rates in nonlinear stochastic difference equation with unbounded noises","volume":"81","author":"Appleby","year":"2009","journal-title":"Stochastics"},{"key":"S146115701300017X_r4","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.02.059"},{"key":"S146115701300017X_r2","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157012000010"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S146115701300017X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T02:27:58Z","timestamp":1559874478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S146115701300017X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":4,"alternative-id":["S146115701300017X"],"URL":"https:\/\/doi.org\/10.1112\/s146115701300017x","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}