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Journal Articles Dynamical Systems and Differential Equations, DCDS Supplement Year : 2017

Abel-type Results for Controlled Piecewise Deterministic Markov Processes

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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Dates and versions

hal-01142323 , version 1 (15-04-2015)

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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. ⟨10.1007/s12591-015-0245-y⟩. ⟨hal-01142323⟩
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