{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:20:27Z","timestamp":1776842427394,"version":"3.51.2"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"260","license":[{"start":{"date-parts":[[2008,4,20]],"date-time":"2008-04-20T00:00:00Z","timestamp":1208649600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation\/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general \u2013 they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank\u2013Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant controls. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here.<\/p>","DOI":"10.1090\/s0025-5718-07-02000-5","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T07:46:03Z","timestamp":1185435963000},"page":"1861-1893","source":"Crossref","is-referenced-by-count":96,"title":["Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations"],"prefix":"10.1090","volume":"76","author":[{"given":"Guy","family":"Barles","sequence":"first","affiliation":[]},{"given":"Espen","family":"Jakobsen","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2007,4,20]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1051\/m2an:2002002","article-title":"On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations","volume":"36","author":"Barles, Guy","year":"2002","journal-title":"M2AN Math. 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