Published Paper

Inserted: 12 jan 2023
Last Updated: 11 sep 2024

Journal: ESAIM Control Optim. Calc. Var.
Volume: 29
Pages: art. 52
Year: 2023
Doi: 10.1051/cocv/2023020

Abstract:

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.