Pith Number

pith:Q4N4LIIY

pith:2026:Q4N4LIIYGMYIXPMOB7EQAXOEER

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Indefinite Stochastic LQ Optimal Control for Jump-Diffusion Systems with Random Coefficients

Qingxin Meng, Xinyu Ma

Under a uniform convexity condition, indefinite stochastic LQ optimal controls exist for jump-diffusion systems with random coefficients and admit closed-loop feedback representations.

arxiv:2605.12775 v1 · 2026-05-12 · math.OC

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Claims

C1strongest claim

Under a uniform convexity condition, we establish the existence and uniqueness of open-loop optimal controls for any initial pair and show that the associated matrix N(t) is uniformly positive definite, yielding an exact closed-loop feedback representation of the optimal control via the SREJ.

C2weakest assumption

The uniform convexity condition must hold globally so that the matrix N(t) remains uniformly positive definite; if it fails for some paths, the existence and closed-loop representation may not hold.

C3one line summary

The paper proves existence and uniqueness of optimal controls for indefinite LQ problems in jump-diffusion systems with random coefficients by constructing a generalized stochastic Riccati equation with jumps from an algebraic inverse flow, under uniform convexity.

References

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[1] Basar, T. and Bernhard, P. (2008). H-infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Springer Science & Business Media. https://doi.org/10.1007/978-0-8176-4757-5 2008 · doi:10.1007/978-0-8176-4757-5

[2] Bismut, J. M. (1976). Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim., 14:419--444. https://doi.org/10.1137/0314028 1976 · doi:10.1137/0314028

[3] Boel, R. and Kohlmann, M. (1980). Semi-martingale models of stochastic optimal control, with applications to double martingales. SIAM J. Control Optim., 18:511--533. https://doi.org/10.1137/0318038 1980 · doi:10.1137/0318038

[4] Chen, S., Li, X. and Zhou, X. Y. (1998). Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim., 36:1685--1702. https://doi.org/10.1137/S0363012996310478 1998 · doi:10.1137/s0363012996310478

[5] Du, K. (2015). Solvability conditions for indefinite linear quadratic optimal stochastic control problems and associated stochastic Riccati equations. SIAM J. Control Optim., 53:3673--3689. https://do 2015 · doi:10.1137/140956051

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:13.219451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

871bc5a11833308bbd8e0fc9005dc424675e2bc5ae084428e3183ccf8d9c91e1

Aliases

arxiv: 2605.12775 · arxiv_version: 2605.12775v1 · doi: 10.48550/arxiv.2605.12775 · pith_short_12: Q4N4LIIYGMYI · pith_short_16: Q4N4LIIYGMYIXPMO · pith_short_8: Q4N4LIIY

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q4N4LIIYGMYIXPMOB7EQAXOEER \
  | 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: 871bc5a11833308bbd8e0fc9005dc424675e2bc5ae084428e3183ccf8d9c91e1

Canonical record JSON

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  "metadata": {
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-12T21:41:32Z",
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