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Math."],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The authors of this paper study approximation methods for stochastic differential equations, and point out a simple relation between the order of convergence in the <jats:italic>p<\/jats:italic>th mean and the order of convergence in the pathwise sense: Convergence in the <jats:italic>p<\/jats:italic>th mean of order \u03b1 for all <jats:italic>p<\/jats:italic> \u2265 1 implies pathwise convergence of order \u03b1 \u2013 \u03b5 for arbitrary \u03b5 &gt; 0. The authors then apply this result to several one-step and multi-step approximation schemes for stochastic differential equations and stochastic delay differential equations. In addition, they give some numerical examples.<\/jats:p>","DOI":"10.1112\/s1461157000001388","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T07:42:31Z","timestamp":1375774951000},"page":"235-253","source":"Crossref","is-referenced-by-count":74,"title":["The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations"],"prefix":"10.1112","volume":"10","author":[{"given":"P.E.","family":"Kloeden","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Neuenkirch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000001388_ref008","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1214\/aop\/1022855419","article-title":"\u2018Asymptotic error distributions for the Euler method for stochastic differential equations\u2019","volume":"26","author":"Jacod","year":"1998","journal-title":"Ann. 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