Abel-type Results for Controlled Piecewise Deterministic Markov Processes

Dan Goreac 1 Oana-Silvia Serea 2
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : In this paper we prove that, in the framework of continuous control problems for piecewise deterministic Markov processes, the existence of a uniform limit for discounted value functions as the discount factor vanishes implies (without any further assumption) the uniform convergence of the value functions with long run average cost as the time horizon increases to infinity. The two limit values coincide. We also provide a converse Tauberian result for a particular class of systems with Poisson-triggered jump mechanism. We exhibit a very simple example in which the dynamics are not dissipative, nevertheless discounted values converge uniformly to a non-constant limit function.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01142323
Contributor : Dan Goreac <>
Submitted on : Wednesday, April 15, 2015 - 12:36:37 AM
Last modification on : Wednesday, September 4, 2019 - 1:52:20 PM

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Dan Goreac, Oana-Silvia Serea. Abel-type Results for Controlled Piecewise Deterministic Markov Processes. Dynamical Systems and Differential Equations, DCDS Supplement, 2017, 25 (1), pp.83--100. ⟨http://link.springer.com/article/10.1007/s12591-015-0245-y⟩. ⟨10.1007/s12591-015-0245-y⟩. ⟨hal-01142323⟩

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