Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems



The present paper aims at studying stochastic singularly perturbed control systems. We begin by recalling the linear (primal and dual) formulations for classical control problems. In this framework, we give necessary and sufficient support criteria for optimality of the measures intervening in these formulations. Motivated by these remarks, in a first step, we provide linearized formulations associated with the value function in the averaged dynamics setting. Second, these formulations are used to infer criteria allowing to identify the optimal trajectory of the averaged stochastic system.


Optimal stochastic control Singularly perturbed Brownian diffusions Occupation measures Linear programming 

Mathematics Subject Classfication

93E20 49J45 49L25 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRSMarne-la-ValléeFrance
  2. 2.Laboratoire de Mathématiques et de Physique, EA 4217Université de Perpignan Via DomitiaPerpignan CedexFrance

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