Pith Number

pith:EFZI3QJ4

pith:2026:EFZI3QJ4MQB2JPXCORQS6DWBNC

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Transportation cost inequalities for mean reflection SPDEs with white noise

Beibei Zhang, Bin Qian

Solutions to mean-reflected SPDEs satisfy a quadratic transportation cost inequality under the uniform norm.

arxiv:2605.17328 v1 · 2026-05-17 · math.PR

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Claims

C1strongest claim

We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution.

C2weakest assumption

The mean-reflected SPDE admits a unique solution whose law satisfies the necessary integrability and continuity properties to make the transportation cost inequality well-defined under the uniform norm (implicit in the abstract's claim that such an inequality can be established for this new equation class).

C3one line summary

Establishes quadratic transportation cost inequality under uniform norm for mean-reflected SPDEs with white noise where reflection depends on the solution's law.

References

33 extracted · 33 resolved · 1 Pith anchors

[1] Transportation cost inequalities for neutral func- tional stochastic equations 2013

[2] Transportation inequalities for stochastic heat equations 2018

[3] A note on Harnack and Transportation inequalities For Stochastic Differential Equations with reflections 2019 · arXiv:1905.01083

[4] G., G¨ otze, F., 1999 1999

[5] G., Houdr´ e, C., 2000 2000

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:52.364837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21728dc13c6403a4bee274612f0ec168945b873046bd8f235276f25f0a739533

Aliases

arxiv: 2605.17328 · arxiv_version: 2605.17328v1 · doi: 10.48550/arxiv.2605.17328 · pith_short_12: EFZI3QJ4MQB2 · pith_short_16: EFZI3QJ4MQB2JPXC · pith_short_8: EFZI3QJ4

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/EFZI3QJ4MQB2JPXCORQS6DWBNC \
  | 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: 21728dc13c6403a4bee274612f0ec168945b873046bd8f235276f25f0a739533

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-17T08:35:17Z",
    "title_canon_sha256": "767fa4961a2dd08ad05e494873c0eb61b5c5bd1d43b9ce703a4e8393978379e1"
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