{"paper":{"title":"Stochastic lattice dynamical systems with fractional noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bj\\\"orn Schmalfu\\ss, Hakima Bessaih, Mar\\'ia J. Garrido-Atienza, Xiaoying Han","submitted_at":"2016-09-08T19:31:33Z","abstract_excerpt":"This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such systems by the Young integration setting and prove that the solution generates a random dynamical system. Further, we analyze the exponential stability of the trivial solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02543","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"}