Singular perturbations and optimal control of stochastic systems in infinite dimension

Abstract: We will discuss a stochastic optimal control problem for a two scale system driven by an infinite dimensional stochastic differential equation which consists of ''slow'' and ''fast'' components. We will consider a rather general case where the evolution is given by an abstract semilinear stochastic differential equation with nonlinear dependence on the controls. We will present a PDE approach to the problem based on the theory of viscosity solutions in Hilbert spaces. This approach allows to prove that as the speed of the fast component goes to infinity, the value functions of the optimal control problems converge to the viscosity solution of a reduced effective equation. Our results generalize to the infinite dimensional case the finite dimensional results of Alvarez and Bardi and complement recent results in Hilbert spaces obtained by Guatteri and Tessitore.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

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