2IECL - Institut Élie Cartan de Lorraine (Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex
Ile du Saulcy - 57 045 Metz Cedex 01 - France)
Abstract : We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to study the link between infinite horizon control of these processes and an optimization problem involving their quasi-stationary distributions and the corresponding extinction rates. More precisely, we obtain an equivalent of the value function when the discount parameter is close to the threshold where the value function becomes infinite , and we characterize the optimal Markov control in this limit. To achieve this, we present a new proof of the dynamic programming principle based upon a pseudo-Markov property for controlled jump processes. We also prove the convergence to a unique quasi-stationary distribution of non-linear branching processes controlled by a Markov control conditioned on non-extinction.
https://hal.inria.fr/hal-01349663
Contributeur : Nicolas Champagnat
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Soumis le : jeudi 28 juillet 2016 - 11:42:08
Dernière modification le : jeudi 6 décembre 2018 - 11:07:06
Document(s) archivé(s) le : samedi 29 octobre 2016 - 11:04:43
Nicolas Champagnat, Julien Claisse. On the link between infinite horizon control and quasi-stationary distributions. Stochastic Processes and their Applications, Elsevier, In press. 〈hal-01349663〉
