Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911033858195456 |
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| author | Gao, Dingqian Lü, Qi |
| author_facet | Gao, Dingqian Lü, Qi |
| contents | In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function. We then prove the existence, uniqueness of viscosity solutions to the HJB equation, along with their continuous dependence on initial data and model parameters. Finally, under appropriate regularity conditions on the value function, we establish a verification theorem that characterizes optimal controls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds Gao, Dingqian Lü, Qi Optimization and Control 93E20, 35D40 In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function. We then prove the existence, uniqueness of viscosity solutions to the HJB equation, along with their continuous dependence on initial data and model parameters. Finally, under appropriate regularity conditions on the value function, we establish a verification theorem that characterizes optimal controls. |
| title | Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds |
| topic | Optimization and Control 93E20, 35D40 |
| url | https://arxiv.org/abs/2507.01407 |