Pith Number

pith:4VEOMNSP

pith:2026:4VEOMNSPMOOSSVNUV5Y7RIPP3Y

not attested not anchored not stored refs pending

Stability of Compensated Jump Integrals under Quadratic Variation Convergence

Philip Kennerberg

Quadratic variation convergence alone implies ucp stability of compensated jump integrals under local linear growth on the integrands.

arxiv:2605.11783 v2 · 2026-05-12 · math.PR

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\pithnumber{4VEOMNSPMOOSSVNUV5Y7RIPP3Y}

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:33.481139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e548e6364f639d2955b4af71f8a1efde30c1cd923469f43d9d688fe90830e370

Aliases

arxiv: 2605.11783 · arxiv_version: 2605.11783v2 · doi: 10.48550/arxiv.2605.11783 · pith_short_12: 4VEOMNSPMOOS · pith_short_16: 4VEOMNSPMOOSSVNU · pith_short_8: 4VEOMNSP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4VEOMNSPMOOSSVNUV5Y7RIPP3Y \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e548e6364f639d2955b4af71f8a1efde30c1cd923469f43d9d688fe90830e370

Canonical record JSON

{
  "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
  }
}