Calculus of Variations and Geometric Measure Theory

M. Bardi - H. Kouhkouh

Singular perturbations in stochastic optimal control with unbounded data

created by bardi on 12 Jan 2023



Inserted: 12 jan 2023

Year: 2022

ArXiv: 2208.00655 PDF


We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neural networks. We construct effective Hamiltonian and initial data and prove the convergence of the value function to the solution of a limit (effective) Cauchy problem for a parabolic equation of HJB type. We use methods of probability, viscosity solutions and homogenization.