{"paper":{"title":"A stochastic invariantization method for It\\^o stochastic perturbations of differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Jacky Cresson, Khadra Nachi, Yasmina Kheloufi","submitted_at":"2018-09-25T08:57:41Z","abstract_excerpt":"In general, adding a stochastic perturbation to a differential equation possessing an invariant manifold destroys the invariance as far as the It\\^o formalism is used. In this article, we propose an invariantization method for perturbations in the It\\^o case which can be used to restore invariance. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. We discuss in particular previous results obtained by Etore and al. in [P. \\'Etor\\'e, S.Labb\\'e , J. Lelong, Long time behaviour of a stochastic nanoparticle, J. Differential Equations 257 (2014), 2115-2135]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09363","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}