{"paper":{"title":"A system of nonlinear equations with application to large deviations for Markov chains with finite lifetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jing Zhang, Wei Sun, Ze-Chun Hu","submitted_at":"2017-05-10T04:02:38Z","abstract_excerpt":"In this paper, we first show the existence of solutions to the following system of nonlinear equations \\begin{eqnarray*}\\left\\{\\begin{array}{l} a_{11}x_1+a_{12}x_2+a_{13}x_3+\\cdots+a_{1n}x_{n} = b_{11}\\frac{1}{x_1}+b_{12}\\frac{1}{x_2}+b_{13}\\frac{1}{x_3}+\\cdots+b_{1n}\\frac{1}{x_{n}},\\\\ a_{21}\\frac{1}{x_1}+a_{22}\\frac{x_2}{x_1}+a_{23}\\frac{x_3}{x_1}+\\cdots+a_{2n}\\frac{x_{n}}{x _1}=b_{21}x_1+b_{22}\\frac{x_1}{x_2}+b_{23}\\frac{x_1}{x_3}+\\cdots+b_{2n}\\frac{x_1}{x_{n}},\\\\ a_{31}\\frac{x_1}{x_2}+a_{32}\\frac{1}{x_2}+a_{33}\\frac{x_3}{x_2}+\\cdots+a_{3n}\\frac{x_{n}}{x _2}=b_{31}\\frac{x_2}{x_1}+b_{32}x_2+b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03601","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"}