Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem
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...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
15.01.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2401.07642 |