{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T06:18:37Z","timestamp":1778739517714,"version":"3.51.4"},"reference-count":33,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["317210226"],"award-info":[{"award-number":["317210226"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper aims to investigate the weak convergence of the Rosenbrock semi-implicit method for semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise.\nWe are interested in SPDEs where the nonlinear part is stronger than the linear part, also called stochastic reaction dominated transport equations.\nFor such SPDEs, many standard numerical schemes lose their stability properties.\nExponential Rosenbrock and Rosenbrock-type methods were proved to be efficient for such SPDEs, but only their strong convergence were recently analyzed.\nHere, we investigate the weak convergence of the Rosenbrock semi-implicit method.\nWe obtain a weak convergence rate which is twice the rate of the strong convergence.\nOur error analysis does not rely on Malliavin calculus, but rather only uses the Kolmogorov equation and the smoothing properties of the resolvent operator resulting from the Rosenbrock semi-implicit approximation.<\/jats:p>","DOI":"10.1515\/cmam-2023-0055","type":"journal-article","created":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T19:51:29Z","timestamp":1706644289000},"page":"467-493","source":"Crossref","is-referenced-by-count":2,"title":["Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6703-3075","authenticated-orcid":false,"given":"Jean Daniel","family":"Mukam","sequence":"first","affiliation":[{"name":"Department of Mathematics , Bielefeld University , 33501 Bielefeld , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1851-1258","authenticated-orcid":false,"given":"Antoine","family":"Tambue","sequence":"additional","affiliation":[{"name":"Department of Computer science, Electrical Engineering and Mathematical Sciences , Western Norway University of Applied Sciences , Inndalsveien 28, 5063 Bergen , Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"2025062712372303763_j_cmam-2023-0055_ref_001","doi-asserted-by":"crossref","unstructured":"A. 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Lindner,\nMalliavin regularity and weak approximation of semilinear SPDEs with L\u00e9vy noise,\nDiscrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 8, 4271\u20134294.","DOI":"10.3934\/dcdsb.2019081"},{"key":"2025062712372303763_j_cmam-2023-0055_ref_005","doi-asserted-by":"crossref","unstructured":"P. R. Beesack,\nMore generalised discrete Gronwall inequalities,\nZAMM Z. Angew. Math. Mech. 65 (1985), no. 12, 583\u2013595.","DOI":"10.1002\/zamm.19850651202"},{"key":"2025062712372303763_j_cmam-2023-0055_ref_006","doi-asserted-by":"crossref","unstructured":"C.-E. Br\u00e9hier and A. Debussche,\nKolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient,\nJ. Math. Pures Appl. (9) 119 (2018), 193\u2013254.","DOI":"10.1016\/j.matpur.2018.08.010"},{"key":"2025062712372303763_j_cmam-2023-0055_ref_007","unstructured":"P.-L. Chow,\nStochastic Partial Differential Equations,\nChapman & Hall\/CRC Appl. Math. Nonlinear Sci. Ser.,\nChapman & Hall\/CRC, Boca Raton, 2007."},{"key":"2025062712372303763_j_cmam-2023-0055_ref_008","doi-asserted-by":"crossref","unstructured":"J. Cui and J. Hong,\nStrong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided Lipschitz coefficient,\nSIAM J. Numer. Anal. 57 (2019), no. 4, 1815\u20131841.","DOI":"10.1137\/18M1215554"},{"key":"2025062712372303763_j_cmam-2023-0055_ref_009","doi-asserted-by":"crossref","unstructured":"G. Da Prato and J. Zabczyk,\nStochastic Equations in Infinite Dimensions,\nEncyclopedia Math. Appl. 152,\nCambridge University, Cambridge, 2014.","DOI":"10.1017\/CBO9781107295513"},{"key":"2025062712372303763_j_cmam-2023-0055_ref_010","doi-asserted-by":"crossref","unstructured":"A. Debussche,\nWeak approximation of stochastic partial differential equations: The nonlinear case,\nMath. 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