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In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential mean-square contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand whether a stochastic linear multistep method can provide an analogous behaviour and which restrictions on the employed stepsize should be imposed in order to reproduce the contractive behaviour. Numerical experiments confirming the theoretical analysis are also given.<\/jats:p>","DOI":"10.1007\/s10444-021-09879-2","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T09:02:48Z","timestamp":1627290168000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Exponential mean-square stability properties of stochastic linear multistep methods"],"prefix":"10.1007","volume":"47","author":[{"given":"Evelyn","family":"Buckwar","sequence":"first","affiliation":[]},{"given":"Raffaele","family":"D\u2019Ambrosio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"9879_CR1","doi-asserted-by":"crossref","unstructured":"Andersson, A., Kruse, R.: Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition, arXiv:1509.00609 (2015)","DOI":"10.1007\/s10543-016-0624-y"},{"issue":"1","key":"9879_CR2","first-page":"261","volume":"101","author":"E Buckwar","year":"2005","unstructured":"Buckwar, E., Horvath-Bokor, R., Winkler, R.: Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations. 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