Optimal control of infinite dimensional two scales stochastic systems

Abstract:

In this talk I will present some results regarding optimal control problems for two-scale, infinite-dimensional, stochastic systems. I will focus on the convergence of the value function as the ratio between the two evolution speeds diverges. The value function is represented as the solution of a backward stochastic differential equation (BSDE) that it is shown to converge towards a reduced BSDE. The limit BSDE involves the solution of an ergodic BSDE and is itself interpreted as the value function of an auxiliary stochastic control problem on a reduced state space.