{"paper":{"title":"Non-Gaussian Limit Theorem for Non-Linear Langevin Equations Driven by L\\'evy Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexei Kulik, Ilya Pavlyukevich","submitted_at":"2017-07-06T20:28:08Z","abstract_excerpt":"In this paper, we study the small noise behaviour of solutions of a non-linear second order Langevin equation $\\ddot x^\\varepsilon_t +|\\dot x^\\varepsilon_t|^\\beta=\\dot Z^\\varepsilon_{\\varepsilon t}$, $\\beta\\in\\mathbb R$, driven by symmetric non-Gaussian L\\'evy processes $Z^\\varepsilon$. This equation describes the dynamics of a one-degree-of-freedom mechanical system subject to non-linear friction and noisy vibrations. For a compound Poisson noise, the process $x^\\varepsilon$ on the macroscopic time scale $t/\\varepsilon$ has a natural interpretation as a non-linear filter which responds to eac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01958","kind":"arxiv","version":2},"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"}