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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.01350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-05T11:12:08Z","cross_cats_sorted":[],"title_canon_sha256":"5d7dc772407b54919e14a9ca65cf9038115a1a8cacd3f8bf9bd537894b7960ef","abstract_canon_sha256":"70c7be73e84aa732876c10bba0592a04191ed7bd46abd46cc36000ac1b4bccf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:26.640775Z","signature_b64":"vEqQ5c6DHdTQL3VYSJsUlF0nTSQLotc54I7pWcgGmQ5GKXm+VeRB3CPDLksIkdbWrQMCBcJYQO2lQEz8Qrz1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62f344de690da45cb44ec7e4531cef0f1bcd82f9ea7fd5688d533c2abd3da342","last_reissued_at":"2026-05-18T00:24:26.640146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:26.640146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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