A dual representation result for value functions in stochastic control of infinite dimensional groups

Viorel Barbu, Mihai Sîrbu

Abstract


We study here the problem of dual representation of the value functions associated to linear-convex stochastic control problems in infinite dimensional Hilbert spaces. Since the dual state runs backwards in time, it turns out that the dual representation has the meaning of a classical (Markov) control problem only if the primal linear state equation is driven by the generator of a group. In the general case, a dual representation of the value function still holds, but such a representation cannot be reduced to solving a dual Hamilton-Jacobi-Bellman equation.

Keywords


value function; Legendre transform; duality

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