{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T18:48:37Z","timestamp":1778525317746,"version":"3.51.4"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"292","license":[{"start":{"date-parts":[[2015,8,12]],"date-time":"2015-08-12T00:00:00Z","timestamp":1439337600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations in one dimension with multiplicative noise under a one-sided Lipschitz condition only. The equation may be additionally coupled with a noisy control variable with global Lipschitz condition but no diffusion. We derive convergence with an implicit rate depending on the regularity of the exact solution. This can be made explicit if the variational solution has more than its canonical spatial regularity. As an application, spatially extended FitzHugh-Nagumo systems with noise are considered.<\/p>","DOI":"10.1090\/s0025-5718-2014-02873-1","type":"journal-article","created":{"date-parts":[[2014,8,14]],"date-time":"2014-08-14T11:52:14Z","timestamp":1408017134000},"page":"743-766","source":"Crossref","is-referenced-by-count":22,"title":["Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition"],"prefix":"10.1090","volume":"84","author":[{"given":"Martin","family":"Sauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wilhelm","family":"Stannat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,8,12]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1142\/S0219025708003191","article-title":"Analysis of the stochastic FitzHugh-Nagumo system","volume":"11","author":"Bonaccorsi, Stefano","year":"2008","journal-title":"Infin. 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