Pith Number

pith:WNE25MUD

pith:2026:WNE25MUDKUFZMNZLCJ7EWS2LDX

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Extended MF-FBSDEs with nonlinear domination-monotonicity conditions and stochastic optimal controls of Linear System with quadruple controls

Hao Wu

Nonlinear adjoint functions extend domination-monotonicity conditions to guarantee well-posedness of extended mean-field FBSDEs and deliver explicit optimal controls for linear systems with quadruple inputs.

arxiv:2605.09374 v2 · 2026-05-10 · math.OC

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Claims

C1strongest claim

Utilizing this generalized well-posedness result for extended MF-FBSDEs in conjunction with other refined analytical techniques, we address two classes of stochastic quadruple optimal controlled problems: a linear-convex problem and a linear-quadratic problem with input constraints that are permitted to be time-dependent and random. For each problem, we establish the existence and uniqueness of optimal controls and derive their explicit closed-form representations.

C2weakest assumption

The nonlinear domination-monotonicity conditions, defined via nonlinear adjoint functions, are sufficient to guarantee well-posedness of the extended MF-FBSDEs.

C3one line summary

Extends domination-monotonicity conditions to nonlinear extended MF-FBSDEs and derives closed-form optimal controls for linear-convex and linear-quadratic stochastic control problems with time-dependent random input constraints.

Receipt and verification

First computed	2026-06-04T01:08:51.085213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b349aeb283550b96372b127e4b4b4b1dfdd853354e91f104dfef85fdd0c8b2b4

Aliases

arxiv: 2605.09374 · arxiv_version: 2605.09374v2 · doi: 10.48550/arxiv.2605.09374 · pith_short_12: WNE25MUDKUFZ · pith_short_16: WNE25MUDKUFZMNZL · pith_short_8: WNE25MUD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WNE25MUDKUFZMNZLCJ7EWS2LDX \
  | 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: b349aeb283550b96372b127e4b4b4b1dfdd853354e91f104dfef85fdd0c8b2b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f610efc29b69e4d46a2dfea8297b79a048ab4ea174b9142fe74cbcde74c012d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-10T06:57:51Z",
    "title_canon_sha256": "b502592fae6b547b278302cbe04049fa2924d097606deaa783e21749f108dc44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09374",
    "kind": "arxiv",
    "version": 2
  }
}