Seminar on Stochastic Differential Equations


Wednesday, 1 August 2007 - 2:00pm to 4:00pm



We will first introduce and justify the classical definition of viscosity solution for the first order Hamilton-Jacobi-Bellman equation in a Hilbert space given in [CL90, CL91] and extending the definition given in [CL83] for the finite dimensional case.We will also recall some classical results that connect the study of the Hamilton-Jacobi-Bellman equations and of a class of optimal control problems: under suitable hypotheses, as in the finite dimensional setting, the value function of the problem comes out to be the only viscosity solution of the Hamilton-Jacobi-Bellman equation. We will eventually present a verification result.