{"paper":{"title":"Ergodicity of stochastic shell models driven by pure jump noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Hakima Bessaih, Paul A. Razafimandimby","submitted_at":"2016-01-13T13:51:15Z","abstract_excerpt":"In the present paper we study a stochastic evolution equation for shell (SABRA \\& GOY) models with pure jump \\levy noise $L=\\sum_{k=1}^\\infty l_k(t)e_k$ on a Hilbert space $\\h$. Here $\\{l_k, k\\in \\mathbb{N}\\}$ is a family of independent and identically distributed (i.i.d.) real-valued pure jump \\levy processes and $\\{e_k, k\\in \\mathbb{N}\\}$ is an orthonormal basis of $\\h$. We mainly prove that the stochastic system has a unique invariant measure. For this aim we show that if the \\levy measure of each component $l_k(t)$ of $L$ satisfies a certain order and a non-{degeneracy} condition and is ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03242","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"}