Pith Number

pith:KB24FNJB

pith:2026:KB24FNJB4PE5WU2F2ZYOGE3FWH

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Mean-Field Backward Stochastic Differential Equations with Nonlinear Resistance and Double Mean Reflections

Hanwu Li, Jin Shi

Mean-field backward SDEs with double mean reflections and nonlinear resistance admit unique solutions for both Lipschitz generators and quadratic generators with bounded terminals.

arxiv:2605.15781 v1 · 2026-05-15 · math.PR

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Claims

C1strongest claim

We establish the existence and uniqueness for both the case of Lipschitz generator and the case where the generator is quadratic and the terminal value is bounded.

C2weakest assumption

The generator satisfies either a global Lipschitz condition or a quadratic growth condition together with a bounded terminal value; these regularity assumptions are invoked to close the fixed-point argument or comparison principle used in the existence proof.

C3one line summary

The paper establishes existence and uniqueness for MFBSDEs with double mean reflections and nonlinear resistance under Lipschitz and quadratic generator assumptions, plus well-posedness for an absolutely continuous variant.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] and El Karoui, N 2004

[2] Buckdahn, R., Djehiche, B., Li, J. and Peng, S. (2009). Mean-field backward stochastic differential equations: a limit approach. The Annals of Probability, 37, 1524–1565 2009

[3] Briand, P., Elie, R. (2013). A simple constructive approach to quadratic BSDEs with or without delay. Stochastic processes and their applications, 123(8), 2921-2939 2013

[4] Briand, P., Elie, R. and Hu, Y. (2018). BSDEs with mean reflection. The Annals of Applied Probability, 28(1), 482-510 2018

[5] Briand, P. and Hibon, H. (2021). Particle systems for mean reflected BSDEs. Stochastic Processes and their Applications, 131, 253-275 2021

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:17.954179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5075c2b521e3c9db5345d670e31365b1f45fbe6f5b9f4d96a30af28b45133bf0

Aliases

arxiv: 2605.15781 · arxiv_version: 2605.15781v1 · doi: 10.48550/arxiv.2605.15781 · pith_short_12: KB24FNJB4PE5 · pith_short_16: KB24FNJB4PE5WU2F · pith_short_8: KB24FNJB

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KB24FNJB4PE5WU2F2ZYOGE3FWH \
  | 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: 5075c2b521e3c9db5345d670e31365b1f45fbe6f5b9f4d96a30af28b45133bf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73f862b950e1c07b9bf3fd5ee4d2a162d627f88cd7a37bae9b05e62dc4c323b7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T09:41:11Z",
    "title_canon_sha256": "0899d9d002c8224272e605d1c38abfa8fb37a1cb7216d7aea649e2963f837618"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15781",
    "kind": "arxiv",
    "version": 1
  }
}