Pith Number

pith:537MKNUQ

pith:2025:537MKNUQE2Z7ZEZ4NMXAEFA5L3

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A Two-fold Randomization Framework for Impulse Control Problems

Haoyang Cao, Yuchao Dong, Zhouhao Yang

Randomized impulse control problems converge to the classical problem as the randomization parameter vanishes.

arxiv:2509.12018 v7 · 2025-09-15 · math.OC

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Claims

C1strongest claim

The randomized impulse control problem converges to its classical counterpart as the randomization parameter λ vanishes; combined with C^{2,α}_loc regularity this confirms the framework provides a robust approximation, and the offline RL algorithm learns the randomized solution which accurately approximates the classical one.

C2weakest assumption

The compound operator formed by the regularized nonlocal operator and regularized stopping operator admits a fixed point, and the equivalent Poisson compound measure scheme is valid for establishing the verification theorem (abstract, paragraph on characterization and verification).

C3one line summary

A randomization framework for impulse control problems derives a semi-linear HJB equation, proves existence and uniqueness, shows convergence to the classical problem as lambda vanishes, and delivers an offline RL algorithm that learns accurate approximations.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:15.521727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eefec5369026b3fc933c6b2e02141d5ef485107eb6957338bd23c7bfed0875c9

Aliases

arxiv: 2509.12018 · arxiv_version: 2509.12018v7 · doi: 10.48550/arxiv.2509.12018 · pith_short_12: 537MKNUQE2Z7 · pith_short_16: 537MKNUQE2Z7ZEZ4 · pith_short_8: 537MKNUQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/537MKNUQE2Z7ZEZ4NMXAEFA5L3 \
  | 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: eefec5369026b3fc933c6b2e02141d5ef485107eb6957338bd23c7bfed0875c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63daa1ee3817a1586c4116d84dc1a6d648ed158841b81dc1f90c1a302a2ef7b3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-09-15T14:58:03Z",
    "title_canon_sha256": "d1bc72ce556938dd1cf602f5f414087d6d9b9e15c44f8bb5dd30f863e07007d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.12018",
    "kind": "arxiv",
    "version": 7
  }
}