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

2024/01/15 by Angeliki Koutsimpela, Koutsimpela, Angeliki, Michail Loulakis +1
Economics, Econometrics and Finance · Engineering · #49L25 #60H30 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2401.07642

openalex publication_date 2024/01/15 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

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.

Related

• On the optimally controlled stochastic shallow lake
• Existence of the optimum for Shallow Lake type models
• Optimal management and spatial patterns in a distributed shallow lake model
• The Finite Horizon impulse control Problem with arbitrary cost functions : the Viscosity Solution Approach
• Mathematical and computational approaches for stochastic control of river environment and ecology: from fisheries viewpoint