2021/03/30 by Guatteri, Giuseppina, Tessitore, Gianmario
#93E20 60H17 #FOS: Mathematics #G.3 #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2103.16152
In this paper we study the limit of the value function for a two-scale, infinite-dimensional, stochastic controlled system with cylindrical noise and possibly degenerate diffusion. The limit is represented as the value function of a new reduced control problem (on a reduced state space). The presence of a cylindrical noise prevents representation of the limit by viscosity solutions of HJB equations, while degeneracy of diffusion coefficients prevents representation as a classical BSDE. We use a vanishing noise regularization technique.