Pith Number

pith:BF6FSKWZ

pith:2026:BF6FSKWZIIKB4QQSDUB7D4JE2W

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Indefinite Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients and Poisson Jumps: Closed-Loop Representation of Open-Loop Optimal Controls

Jiaqiang Wen, Jie Xiong, Kai Ding, Xin Zhang

Under a uniform convexity condition, the stochastic Riccati equation with Poisson jumps admits a unique strongly regular solution that gives open-loop optimal controls a closed-loop representation.

arxiv:2605.13204 v1 · 2026-05-13 · math.OC

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Claims

C1strongest claim

Under a uniform convexity condition on the cost functional, we prove that the associated stochastic Riccati equation (SRE) with jumps admits a unique strongly regular solution. As a consequence, the open-loop optimal control admits a closed-loop representation.

C2weakest assumption

The uniform convexity condition on the cost functional is assumed to hold; the proof relies on this to establish existence and strong regularity of the SRE solution.

C3one line summary

Under uniform convexity, the stochastic Riccati equation with jumps has a unique strongly regular solution, enabling closed-loop representation of optimal controls in indefinite stochastic LQ problems with random coefficients and Poisson jumps.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] M. Ait Rami, J. B. Moore, and X. Y. Zhou. Indefinite stochastic linear quadratic control and generalized differential Riccati equation.SIAM Journal on Control and Optimization, 40:1296–1311, 2002 2002

[2] M. Athans. The role and use of the stochastic linear-quadratic-gaussian problem in control system design.IEEE Transactions on Automatic Control, 16(6):529–552, 1971 1971

[3] A. Bensoussan. Lectures on stochastic control. InNonlinear Filtering and Stochastic Control, volume 972 ofLecture Notes in Mathematics, pages 1–62. Springer, 1982 1982

[4] J.-M. Bismut. Linear quadratic optimal stochastic control with random coefficients.SIAM Journal on Control and Optimization, 14:419–444, 1976 1976

[5] J.-M. Bismut. Contrˆ ole des syst` emes lin´ eaires quadratiques: Applications de l’int´ egrale stochastique. InS´ eminaire de Probabilit´ es, XII, volume 649 ofLecture Notes in Mathematics, pages 180 1978

Formal links

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Receipt and verification

First computed	2026-05-18T03:08:48.629755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

097c592ad942141e42121d03f1f124d5b83eae9118b2b847fabd2647c7e29a7c

Aliases

arxiv: 2605.13204 · arxiv_version: 2605.13204v1 · doi: 10.48550/arxiv.2605.13204 · pith_short_12: BF6FSKWZIIKB · pith_short_16: BF6FSKWZIIKB4QQS · pith_short_8: BF6FSKWZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BF6FSKWZIIKB4QQSDUB7D4JE2W \
  | 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: 097c592ad942141e42121d03f1f124d5b83eae9118b2b847fabd2647c7e29a7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43c4b1be265bffb1c9e8a9ebda6dd000a9fe196dca530c9bc613a0fcd1c5c800",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-13T08:56:29Z",
    "title_canon_sha256": "23e071cc1215b363590af57a87bf17d64e6eac3d85f38f713e5734b50f1d2a86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13204",
    "kind": "arxiv",
    "version": 1
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}