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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04478 |
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| _version_ | 1866914448186277888 |
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| author | Lin, Yongpeng Meng, Qingxin Tang, Maoning |
| author_facet | Lin, Yongpeng Meng, Qingxin Tang, Maoning |
| contents | This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash equilibria. When weighting matrices are indefinite, the classical first-order conditions are no longer sufficient for optimality; we introduce a global nonnegativity condition to restore sufficiency, which becomes a cornerstone of the subsequent analysis. To characterize the equilibria explicitly, we develop fully coupled forward-backward stochastic difference equations and a system of non-symmetric stochastic Riccati equations (FBS$Δ$Es) with constraints. that decouple the stochastic Hamiltonian system. A key technical contribution is the provision of sufficient conditions -- positive semidefiniteness of the Riccati matrices operators and structural non-degeneracy -- that guarantee the invertibility of a related operator, ensuring the well-posedness of the closed-loop feedback representation of the open-loop Nash equilibrium strategies. A distinctive feature of this work is the presence of fully random coefficients, which leads to fully nonlinear higher-order backward stochastic difference equations in the Riccati framework, in contrast to the algebraic Riccati equations in the deterministic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Viscosity Solutions of Hamilton--Jacobi--Bellman Equations for Control Systems Driven by Teugels Martingales Lin, Yongpeng Meng, Qingxin Tang, Maoning Optimization and Control This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash equilibria. When weighting matrices are indefinite, the classical first-order conditions are no longer sufficient for optimality; we introduce a global nonnegativity condition to restore sufficiency, which becomes a cornerstone of the subsequent analysis. To characterize the equilibria explicitly, we develop fully coupled forward-backward stochastic difference equations and a system of non-symmetric stochastic Riccati equations (FBS$Δ$Es) with constraints. that decouple the stochastic Hamiltonian system. A key technical contribution is the provision of sufficient conditions -- positive semidefiniteness of the Riccati matrices operators and structural non-degeneracy -- that guarantee the invertibility of a related operator, ensuring the well-posedness of the closed-loop feedback representation of the open-loop Nash equilibrium strategies. A distinctive feature of this work is the presence of fully random coefficients, which leads to fully nonlinear higher-order backward stochastic difference equations in the Riccati framework, in contrast to the algebraic Riccati equations in the deterministic setting. |
| title | Viscosity Solutions of Hamilton--Jacobi--Bellman Equations for Control Systems Driven by Teugels Martingales |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.04478 |