Pith Number

pith:WJRRWH36

pith:2026:WJRRWH36E7W5BPN2N5WNBOFPZL

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Bridging classical and martingale Schr\"odinger bridges

Armand Ley, Giorgia Bifronte, Julio Backhoff, Mathias Beiglb\"ock

The continuous martingale Schrödinger bridge coincides with the Föllmer martingale in the irreducible case.

arxiv:2604.01299 v2 · 2026-04-01 · math.PR · q-fin.MF

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Record completeness

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Claims

C1strongest claim

In the irreducible case, we prove that this continuous martingale Schrödinger bridge coincides with the Föllmer martingale, that is, with the Doob martingale associated to a suitable Föllmer process.

C2weakest assumption

The probability measures are in convex order and the setup is irreducible for the claimed coincidence with the Föllmer martingale; these are invoked as prerequisites for the equivalences and characterizations.

C3one line summary

Martingale Schrödinger bridges extend to any dimension, minimize weighted quadratic energy from Brownian motion in continuous time, and coincide with Föllmer martingales in irreducible cases.

References

52 extracted · 52 resolved · 2 Pith anchors

[1] B. Acciaio, A. Marini, and G. Pammer. Calibration of the bass local volatility model.ArXiv e-prints, 2311.14567, 2023 2023

[2] J.-J. Alibert, G. Bouchitté, and T. Champion. A new class of costs for optimal transport planning.European Journal of Applied Mathematics, 30(6):1229–1263, 2019 2019

[3] A. Alouadi, A. Barreau, G. Carlier, and H. Pham. Robust time series generation via schr"odinger bridge. 2025 2025

[4] LightSBB-M: Bridging Schr\"odinger and Bass for Generative Diffusion Modeling 2026 · arXiv:2601.19312

[5] A. Alouadi, P. Henry-Labord‘ere, G. Loeper, O. Mazhar, H. Pham, and N. Touzi. Lightsbb-m: Bridging schr"odinger and bass for generative diffusion modeling. 2026 2026

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:22.457610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2631b1f7e27edd0bdba6f6cd0b8afcae8ed2ab7f657bfeca5b83cc42dcbef69

Aliases

arxiv: 2604.01299 · arxiv_version: 2604.01299v2 · doi: 10.48550/arxiv.2604.01299 · pith_short_12: WJRRWH36E7W5 · pith_short_16: WJRRWH36E7W5BPN2 · pith_short_8: WJRRWH36

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WJRRWH36E7W5BPN2N5WNBOFPZL \
  | 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: b2631b1f7e27edd0bdba6f6cd0b8afcae8ed2ab7f657bfeca5b83cc42dcbef69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d8adb6f3378828a6d4a8db5b130db4aaeca80ab4d62e8b219c7377be6524e0e",
    "cross_cats_sorted": [
      "q-fin.MF"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-01T18:04:48Z",
    "title_canon_sha256": "43828bd9649136c88c6f8699c9c029aee1b15867326d5c51e3a7597de7d01495"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.01299",
    "kind": "arxiv",
    "version": 2
  }
}