Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914642938298368 |
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| author | Koutsimpela, Angeliki Loulakis, Michail |
| author_facet | Koutsimpela, Angeliki Loulakis, Michail |
| contents | We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem Koutsimpela, Angeliki Loulakis, Michail Optimization and Control Probability 93E20, 60H30, 49L25 We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake problem. |
| title | Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem |
| topic | Optimization and Control Probability 93E20, 60H30, 49L25 |
| url | https://arxiv.org/abs/2401.07642 |