Applied Mathematics & Optimization

, Volume 68, Issue 2, pp 181–217 | Cite as

Stochastic Maximum Principle for Optimal Control of SPDEs

  • Marco Fuhrman
  • Ying HuEmail author
  • Gianmario Tessitore


We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form that allows direct applications to a large class of controlled stochastic parabolic equations. We allow for a diffusion coefficient dependent on the control parameter, and the space of control actions is general, so that in particular we need to introduce two adjoint processes. The second adjoint process takes values in a suitable space of operators on L 4.


Stochastic maximum principle Stochastic partial differential equation Optimal control Adjoint process 



The authors wish to thank the referee for his valuable and precise comments.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.IRMARUniversité Rennes 1Rennes CedexFrance
  3. 3.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly

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