{"paper":{"title":"On cubic difference equations with variable coefficients and fading stochastic perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexandra Rodkina, C\\'onall Kelly, Ricardo Baccas","submitted_at":"2018-02-05T11:12:08Z","abstract_excerpt":"We consider the stochastically perturbed cubic difference equation with variable coefficients \\[ x_{n+1}=x_n(1-h_nx_n^2)+\\rho_{n+1}\\xi_{n+1}, \\quad n\\in \\mathbb N,\\quad x_0\\in \\mathbb R. \\] Here $(\\xi_n)_{n\\in \\mathbb N}$ is a sequence of independent random variables, and $(\\rho_n)_{n\\in \\mathbb N}$ and $(h_n)_{n\\in \\mathbb N}$ are sequences of nonnegative real numbers. We can stop the sequence $(h_n)_{n\\in \\mathbb N}$ after some random time $\\mathcal N$ so it becomes a constant sequence, where the common value is an $\\mathcal{F}_\\mathcal{N}$-measurable random variable. We derive conditions on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01350","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"}