On the link between infinite horizon control and quasi-stationary distributions

Nicolas Champagnat 1, 2 Julien Claisse 3
1 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
Type de document :
Pré-publication, Document de travail
2016
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Dernière modification le : jeudi 11 janvier 2018 - 16:48:53
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Distributed under a Creative Commons Paternité 4.0 International License

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  • HAL Id : hal-01349663, version 1
  • ARXIV : 1607.08046

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Nicolas Champagnat, Julien Claisse. On the link between infinite horizon control and quasi-stationary distributions. 2016. 〈hal-01349663〉

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