Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

Rainer Buckdahn 1, 2 Dan Goreac 3 Marc Quincampoix 1
1 LM - Laboratoire de mathématiques de Brest
2 Institute for Advanced Study Jinan
3 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : We consider an optimal stochastic control problem for which the payoff is the average of a given cost function. In a non ergodic setting, but under a suitable nonexpansivity condition, we obtain the existence of the limit value when the averaging parameter converges (namely the discount factor tends to zero for Abel mean or the horizon tends to infi nity for the Ces aro mean). The main novelty of our result lies on the fact that this limit may depend on initial conditions of the control system (in contrast to what is usually obtained by other approaches). We also prove that the limit does not depend of the chosen average (Abel or Ces aro mean).
Keywords : Stochastic control Asymptotic value function Uniform Abel-Tauberian theorems Occupation measures
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Journal articles
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https://hal-upec-upem.archives-ouvertes.fr/hal-00879274
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Submitted on : Saturday, November 2, 2013 - 1:51:07 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:20 PM

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Rainer Buckdahn, Dan Goreac, Marc Quincampoix. Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems. Applied Mathematics and Optimization, Springer Verlag (Germany), 2014, 70 (1), pp.1--28. ⟨10.1007/s00245-013-9230-4⟩. ⟨hal-00879274⟩

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