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Ergodic Maximum Principle for Stochastic Systems

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, Rome, 00185, Italy

    Carlo Orrieri

  2. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 55, Milan, 20125, Italy

    Gianmario Tessitore

  3. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou věží 4, Prague 8, 182 08, Czech Republic

    Petr Veverka

Authors
  1. Carlo Orrieri
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  2. Gianmario Tessitore
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  3. Petr Veverka
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Correspondence to Carlo Orrieri.

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Orrieri, C., Tessitore, G. & Veverka, P. Ergodic Maximum Principle for Stochastic Systems. Appl Math Optim 79, 567–591 (2019). https://doi.org/10.1007/s00245-017-9448-7

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