Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem
Optimization and Control
2024-01-18 v1 Probability
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.
Cite
@article{arxiv.2401.07642,
title = {Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem},
author = {Angeliki Koutsimpela and Michail Loulakis},
journal= {arXiv preprint arXiv:2401.07642},
year = {2024}
}