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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","authors_text":"Philip Kennerberg","cross_cats":[],"headline":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-12T08:50:24Z","title":"Stability of Compensated Jump Integrals under Quadratic Variation Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.11783","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T05:20:13.124028Z","id":"ceba67b5-cada-4f72-8878-cbff5510d5d6","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.","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.","weakest_assumption":"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."}},"verdict_id":"ceba67b5-cada-4f72-8878-cbff5510d5d6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fe818b824a6a731217294db5407d39edd13610b81cb2cf0c619f8185d2c46c5f","target":"record","created_at":"2026-05-26T01:03:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2c0c4b2c321647a125e8ab11a3a938aa970da78968e16b33e53086d6a665059e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-12T08:50:24Z","title_canon_sha256":"c0ec0dc73b6bfd27775f1360b43b70b615992972970cf736dedadb65ec682016"},"schema_version":"1.0","source":{"id":"2605.11783","kind":"arxiv","version":2}},"canonical_sha256":"e548e6364f639d2955b4af71f8a1efde30c1cd923469f43d9d688fe90830e370","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e548e6364f639d2955b4af71f8a1efde30c1cd923469f43d9d688fe90830e370","first_computed_at":"2026-05-26T01:03:33.481139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:33.481139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzALCuO/FSeVxBXyPXHloTLZd9kvW0MMwOmGmdzEQsjab7yOFnPLbuQAdftgris7vZjt/0iOUpOjqL8uir6XDw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:33.481987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.11783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe818b824a6a731217294db5407d39edd13610b81cb2cf0c619f8185d2c46c5f","sha256:5913efbfd2bca904ea998d485d8bf0e3eb324a22c2a7bfeb370d2e5000cf8a0a"],"state_sha256":"8d86708888d2a1a549f55d3c4af20502c6a65727f3f93e3102c27bc727a09931"}