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Let \\(X\\) and \\(\\{X^n\\}_{n\\ge1}\\) be c\\`adl\\`ag processes with jump measures \\(\\mu,\\mu_n\\) and predictable compensators \\(\\nu,\\nu_n\\). Under the assumption \\[ [X^n-X]_t \\to 0 \\qquad\\text{in probability}, \\] we establish ucp convergence of compensated jump integrals of the form \\[ \\int_0^. \\int_{\\mathbb R} f_n(s,x)(\\mu_n-\\nu_n)(ds,dx) \\] under local linear growth and locally uniform convergence assumptions on the integrands.\n  The proof is based on two structural mechanisms. The first is a forbi"},"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":true},"canonical_record":{"source":{"id":"2605.11783","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-12T08:50:24Z","cross_cats_sorted":[],"title_canon_sha256":"c0ec0dc73b6bfd27775f1360b43b70b615992972970cf736dedadb65ec682016","abstract_canon_sha256":"2c0c4b2c321647a125e8ab11a3a938aa970da78968e16b33e53086d6a665059e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:33.481987Z","signature_b64":"SzALCuO/FSeVxBXyPXHloTLZd9kvW0MMwOmGmdzEQsjab7yOFnPLbuQAdftgris7vZjt/0iOUpOjqL8uir6XDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e548e6364f639d2955b4af71f8a1efde30c1cd923469f43d9d688fe90830e370","last_reissued_at":"2026-05-26T01:03:33.481139Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:33.481139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of Compensated Jump Integrals under Quadratic Variation Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Kennerberg","submitted_at":"2026-05-12T08:50:24Z","abstract_excerpt":"We study the stability of compensated jump integrals under convergence of quadratic variation alone. Let \\(X\\) and \\(\\{X^n\\}_{n\\ge1}\\) be c\\`adl\\`ag processes with jump measures \\(\\mu,\\mu_n\\) and predictable compensators \\(\\nu,\\nu_n\\). Under the assumption \\[ [X^n-X]_t \\to 0 \\qquad\\text{in probability}, \\] we establish ucp convergence of compensated jump integrals of the form \\[ \\int_0^. \\int_{\\mathbb R} f_n(s,x)(\\mu_n-\\nu_n)(ds,dx) \\] under local linear growth and locally uniform convergence assumptions on the integrands.\n  The proof is based on two structural mechanisms. The first is a forbi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under the assumption [X^n - X]_t → 0 in probability, we establish ucp convergence of compensated jump integrals of the form ∫_0^. ∫_R f_n(s,x)(μ_n - ν_n)(ds,dx) under local linear growth and locally uniform convergence assumptions on the integrands.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The integrands f_n satisfy local linear growth and locally uniform convergence; the forbidden bands principle and compensator mass control hold based on quadratic variation convergence alone.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quadratic variation convergence alone implies ucp convergence of compensated jump integrals for cadlag processes under local linear growth and locally uniform integrand conditions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ce02aa37b7aeef6f0e220c485c383ed621ac9b0ea1eaa0693db079fda84e6383"},"source":{"id":"2605.11783","kind":"arxiv","version":2},"verdict":{"id":"ceba67b5-cada-4f72-8878-cbff5510d5d6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T05:20:13.124028Z","strongest_claim":"Under the assumption [X^n - X]_t → 0 in probability, we establish ucp convergence of compensated jump integrals of the form ∫_0^. ∫_R f_n(s,x)(μ_n - ν_n)(ds,dx) under local linear growth and locally uniform convergence assumptions on the integrands.","one_line_summary":"Quadratic variation convergence alone implies ucp convergence of compensated jump integrals for cadlag processes under local linear growth and locally uniform integrand conditions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The integrands f_n satisfy local linear growth and locally uniform convergence; 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