{"paper":{"title":"Efficient Simulation for Branching Linear Recursions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto, Ningyuan Chen","submitted_at":"2015-03-31T18:20:01Z","abstract_excerpt":"We consider a linear recursion of the form $$R^{(k+1)}\\stackrel{\\mathcal D}{=}\\sum_{i=1}^{N}C_iR^{(k)}_i+Q,$$ where $(Q,N,C_1,C_2,\\dots)$ is a real-valued random vector with $N\\in\\mathbb{N}=\\{0, 1, 2, \\dots\\}$, $\\{R^{(k)}_i\\}_{i\\in\\mathbb{N}}$ is a sequence of i.i.d. copies of $R^{(k)}$, independent of $(Q,N,C_1,C_2,\\dots)$, and $\\stackrel{\\mathcal{D}}{=}$ denotes equality in distribution. For suitable vectors $(Q,N,C_1,C_2,\\dots)$ and provided the initial distribution of $R^{(0)}$ is well-behaved, the process $R^{(k)}$ is known to converge to the endogenous solution of the corresponding stoch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09150","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"}