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The main novelty with respect to the related literature is that we consider SDEs in the It\u00f4 sense, with progressively measurable coefficients, for which an explicit It\u00f4-Stratonovich conversion is not available. We prove convergence of the Magnus expansion up to a stopping time<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\tau $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c4<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and provide a novel asymptotic estimate of the cumulative distribution function of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\tau $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c4<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. As an application, we propose a new method for the numerical solution of stochastic partial differential equations (SPDEs) based on spatial discretization and application of the stochastic Magnus expansion. A notable feature of the method is that it is fully parallelizable. We also present numerical tests in order to asses the accuracy of the numerical schemes.<\/jats:p>","DOI":"10.1007\/s10915-021-01633-6","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:07:34Z","timestamp":1634602054000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On the Stochastic Magnus Expansion and Its Application to SPDEs"],"prefix":"10.1007","volume":"89","author":[{"given":"Kevin","family":"Kamm","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4329-7054","authenticated-orcid":false,"given":"Stefano","family":"Pagliarani","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8837-5568","authenticated-orcid":false,"given":"Andrea","family":"Pascucci","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,18]]},"reference":[{"key":"1633_CR1","doi-asserted-by":"crossref","unstructured":"Azencott, R.: Formule de Taylor stochastique et d\u00e9veloppement asymptotique d\u2019int\u00e9grales de Feynman. 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