{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T18:00:02Z","timestamp":1781287202422,"version":"3.54.1"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"361","license":[{"start":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T00:00:00Z","timestamp":1781568000000},"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 the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations; e.g.\u00a0robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e.\u00a0in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e.\u00a0time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion approximations.<\/p>","DOI":"10.1090\/mcom\/4112","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T10:17:36Z","timestamp":1750069056000},"page":"2481-2514","source":"Crossref","is-referenced-by-count":1,"title":["On time uniform Wong-Zakai approximation theorems"],"prefix":"10.1090","volume":"95","author":[{"given":"Pierre","family":"Del Moral","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shulan","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ajay","family":"Jasra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamza","family":"Ruzayqat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinyu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2025,6,16]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1080\/07362998408809031","article-title":"An approach to Ito linear equations in Hilbert spaces by approximation of white noise with coloured noise","volume":"2","author":"Acquistapace, P.","year":"1984","journal-title":"Stochastic Anal. 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