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has been cited by the following article:

• TITLE: On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

  AUTHORS: Mario Annunziato, Alfio Borzì, Fabio Nobile, Raul Tempone

  KEYWORDS: Hamilton-Jacobi-Bellman Equation, Fokker-Planck Equation, Optimal Control Theory, Stochastic Differential Equations, Hybrid Systems

  JOURNAL NAME: Applied Mathematics, Vol.5 No.16, September 2, 2014

  ABSTRACT: In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the Fokker-Planck formalism allows considering a larger classof objectives. To illustratethe connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.