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arXiv · 2401.07642

Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

Angeliki Koutsimpela·Michail Loulakis
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Abstract

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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Angeliki Koutsimpela, Michail Loulakis. 2024-01-15. Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem. https://arxiv.org/abs/2401.07642

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