Applied Mathematics & Optimization

, Volume 79, Issue 3, pp 567–591 | Cite as

Ergodic Maximum Principle for Stochastic Systems

  • Carlo OrrieriEmail author
  • Gianmario Tessitore
  • Petr Veverka


We present a version of the stochastic maximum principle (SMP) for ergodic control problems. In particular we give necessary (and sufficient) conditions for optimality for controlled dissipative systems in finite dimensions. The strategy we employ is mainly built on duality techniques. We are able to construct a dual process for all positive times via the analysis of a suitable class of perturbed linearized forward equations. We show that such a process is the unique bounded solution to a backward SDE on infinite horizon from which we can write a version of the SMP.


Stochastic maximum principle Stochastic ergodic control problems Dissipative systems Backward stochastic differential equation 

Mathematics Subject Classification

60H15 93E20 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Carlo Orrieri
    • 1
    Email author
  • Gianmario Tessitore
    • 2
  • Petr Veverka
    • 3
  1. 1.Dipartimento di MatematicaSapienza Università di RomaRomeItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanItaly
  3. 3.Institute of Information Theory and AutomationCzech Academy of SciencesPrague 8Czech Republic

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