{"paper":{"title":"Setvalued dynamical systems for stochastic evolution equations driven by fractional noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Schmalfuss, J. Valero, M.J. Garrido-Atienza","submitted_at":"2019-03-05T07:07:03Z","abstract_excerpt":"We consider Hilbert-valued evolution equations driven by H\\\"{o}lder paths with H\\\"{o}lder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be enough to ensure the uniqueness of solutions. Nevertheless, adopting a multivalued setting, we will prove that the set of all solutions corresponding to the same initial condition generates a (multivalued) nonautonomous dynamical system $\\Phi$. Finally, to prove that $\\Phi$ is measurable (and hence a (multivalued) random dynamical system), we need to construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01702","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"}