Pith Number

pith:UYRLBPFP

pith:2026:UYRLBPFPSIOXR2WMZEYLRRDHJW

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Stochastic integration with respect to a L\'evy basis

Markus Riedle

Decoupling inequalities for tangent sequences reduce stochastic integration with respect to a Lévy basis to deterministic integration of infinitely divisible measures.

arxiv:2605.16072 v1 · 2026-05-15 · math.PR

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Claims

C1strongest claim

We develop a stochastic integration theory for predictable integrands with respect to a Lévy basis. Our approach is based on decoupling inequalities for tangent sequences and reduces the construction of the stochastic integral essentially to the deterministic integration theory for infinitely divisible random measures developed by Rajput and Rosiński.

C2weakest assumption

The construction relies on the applicability of decoupling inequalities for tangent sequences to the predictable integrands and the Lévy basis under consideration, as stated in the abstract's description of the approach.

C3one line summary

Develops stochastic integration for predictable processes w.r.t. Lévy basis via decoupling inequalities, reducing to Rajput-Rosiński deterministic theory, with characterization via semimartingale characteristics and Musielak-Orlicz structure.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] R. M. Balan. SPDEs withα-stable L´ evy noise: a random field approach. Int. J. Stoch. Anal., pages Art. ID 793275, 22, 2014 2014

[2] R. M. Balan and J. J. Jim´ enez. Series expansions for stochastic partial dif- ferential equations with symmetricα-stable L´ evy noise.J. Theoret. Probab., 38(3):Paper No. 64, 63, 2025 2025

[3] Bichteler.Stochastic integration with jumps 2002

[4] K. Bichteler and J. Jacod. Random measures and stochastic integration. InTheory and application of random fields (Bangalore, 1982), volume 49 of Lect. Notes Control Inf. Sci., pages 1–18. Springer-Ver 1982

[5] Bod´ o and M 2025

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:51.454150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a622b0bcaf921d78eaccc930b8c4674d982495dbffee90e9e98c248b83af54c8

Aliases

arxiv: 2605.16072 · arxiv_version: 2605.16072v1 · doi: 10.48550/arxiv.2605.16072 · pith_short_12: UYRLBPFPSIOX · pith_short_16: UYRLBPFPSIOXR2WM · pith_short_8: UYRLBPFP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UYRLBPFPSIOXR2WMZEYLRRDHJW \
  | 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: a622b0bcaf921d78eaccc930b8c4674d982495dbffee90e9e98c248b83af54c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e6e4f74c3a6c65d2bef0d8e462967ad9a067e08a230584fbb42a3da5bfd688b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T15:34:48Z",
    "title_canon_sha256": "c08a9879c60b923082e93c6a776a2bb8f12f6c90637738cb0188a50fac06b2fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16072",
    "kind": "arxiv",
    "version": 1
  }
}