{"paper":{"title":"AR(1) sequence with random coefficients: Regenerative properties and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Koushik Saha, Krishna B. Athreya, Radhendushka Srivastava","submitted_at":"2017-09-12T09:18:58Z","abstract_excerpt":"Let $\\{X_n\\}_{n\\ge0}$ be a sequence of real valued random variables such that $X_n=\\rho_n X_{n-1}+\\epsilon_n,~n=1,2,\\ldots$, where $\\{(\\rho_n,\\epsilon_n)\\}_{n\\ge1}$ are i.i.d. and independent of initial value (possibly random) $X_0$. In this paper it is shown that, under some natural conditions on the distribution of $(\\rho_1,\\epsilon_1)$, the sequence $\\{X_n\\}_{n\\ge0}$ is regenerative in the sense that it could be broken up into i.i.d. components. Further, when $\\rho_1$ and $\\epsilon_1$ are independent, we construct a non-parametric strongly consistent estimator of the characteristic function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03753","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"}