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For this purpose, we propose explicit stochastic Poisson integrators based on a splitting strategy, and analyse their qualitative and quantitative properties: preservation of Casimir functions, existence of almost sure or moment bounds, asymptotic preserving property, and strong and weak rates of convergence. The construction of the schemes and the theoretical results are illustrated through extensive numerical experiments for three examples of stochastic Lie\u2013Poisson systems, namely: stochastically perturbed Maxwell\u2013Bloch, rigid body and sine\u2013Euler equations.<\/p>","DOI":"10.1090\/mcom\/3829","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T10:40:24Z","timestamp":1675248024000},"page":"2167-2216","source":"Crossref","is-referenced-by-count":7,"title":["Splitting integrators for stochastic Lie\u2013Poisson systems"],"prefix":"10.1090","volume":"92","author":[{"given":"Charles-Edouard","family":"Br\u00e9hier","sequence":"first","affiliation":[]},{"given":"David","family":"Cohen","sequence":"additional","affiliation":[]},{"given":"Tobias","family":"Jahnke","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,4,27]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"A1800--A1823","DOI":"10.1137\/110846609","article-title":"High weak order methods for stochastic differential equations based on modified equations","volume":"34","author":"Abdulle, Assyr","year":"2012","journal-title":"SIAM J. 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