{"paper":{"title":"Large deviation for lasso diffusion process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Azzouz Dermoune, Khalifa Es-Sebaiy, Youssef Ouknine","submitted_at":"2016-10-01T21:47:58Z","abstract_excerpt":"The aim of the present paper is to extend the large deviation with discontinuous statistics studied in \\cite{BDE} to the diffusion $d\\mathbf{x}^\\varepsilon = -\\{\\mathbf{A}^\\top (\\mathbf{A} \\mathbf{x}^\\varepsilon - \\mathbf{y}) + \\mu sgn(\\mathbf{x}^\\varepsilon)\\}dt + \\varepsilon d\\mathbf{w}$. The discontinuity of the drift of the diffusion discussed in \\cite{BDE} is equal to the hyperplane $\\{\\mathbf{x} \\in \\mathbb{R}^d:\\ x_1=0\\}$, however, in our case the discontinuity is more complex and is equal to the set $\\{\\mathbf{x} \\in \\mathbb{R}^d:\\  \\prod_{i=1}^dx_i=0\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00194","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"}