Volume 26, 2020
|Number of page(s)||18|
|Published online||25 February 2020|
Optimal control on graphs: existence, uniqueness, and long-term behavior*
Université Paris 1 Panthéon-Sorbonne, Centre d’Economie de la Sorbonne,
106, Boulevard de l’Hôpital,
** Corresponding author: firstname.lastname@example.org
Accepted: 20 November 2019
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with results on the associated ergodic Hamilton-Jacobi equation.
Mathematics Subject Classification: 05C81 / 34E05 / 49L20 / 90C40 / 93E20
Key words: Optimal control / graphs / asymptotic analysis / Ergodic Hamilton-Jacobi equation
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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