Infinite Horizon Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations and Their Application to LQ Optimal Control Problems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916804524244992 |
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| author | Ma, Xinyu Li, Xun Meng, Qingxin |
| author_facet | Ma, Xinyu Li, Xun Meng, Qingxin |
| contents | This paper focuses on the study of infinite horizon fully coupled nonlinear forward-backward stochastic difference equations (FBS$\bigtriangleup$Es). Firstly, we establish a pair of priori estimates for the solutions to forward stochastic difference equations (S$\bigtriangleup$Es) and backward stochastic difference equations (BS$\bigtriangleup$Es), respectively. Then, to achieve broader applicability, we utilize a set of domination-monotonicity conditions that are more lenient than standard assumptions. Using these conditions, we apply continuation methods to prove the unique solvability of infinite horizon fully coupled FBS$\bigtriangleup$Es and derive a set of solution estimates. Furthermore, our results have considerable implications for a variety of related linear quadratic (LQ) problems, especially when the stochastic Hamiltonian system is consistent with FBS$\bigtriangleup$Es satisfying the introduced domination-monotonicity conditions. Thus, by solving the associated stochastic Hamiltonian system, we explicitly characterize the unique optimal control. This is the first work establishing solvability of fully coupled nonlinear FBS$\bigtriangleup$Es under domination-monotonicity conditions in infinite horizon discrete-time setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Horizon Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations and Their Application to LQ Optimal Control Problems Ma, Xinyu Li, Xun Meng, Qingxin Optimization and Control This paper focuses on the study of infinite horizon fully coupled nonlinear forward-backward stochastic difference equations (FBS$\bigtriangleup$Es). Firstly, we establish a pair of priori estimates for the solutions to forward stochastic difference equations (S$\bigtriangleup$Es) and backward stochastic difference equations (BS$\bigtriangleup$Es), respectively. Then, to achieve broader applicability, we utilize a set of domination-monotonicity conditions that are more lenient than standard assumptions. Using these conditions, we apply continuation methods to prove the unique solvability of infinite horizon fully coupled FBS$\bigtriangleup$Es and derive a set of solution estimates. Furthermore, our results have considerable implications for a variety of related linear quadratic (LQ) problems, especially when the stochastic Hamiltonian system is consistent with FBS$\bigtriangleup$Es satisfying the introduced domination-monotonicity conditions. Thus, by solving the associated stochastic Hamiltonian system, we explicitly characterize the unique optimal control. This is the first work establishing solvability of fully coupled nonlinear FBS$\bigtriangleup$Es under domination-monotonicity conditions in infinite horizon discrete-time setting. |
| title | Infinite Horizon Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations and Their Application to LQ Optimal Control Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.04603 |