Volume 29, 2023
|Number of page(s)||25|
|Published online||03 July 2023|
Singular perturbations in stochastic optimal control with unbounded data
Department of Mathematics “T. Levi-Civita”, University of Padova, via Trieste, 63, 35121 Padova, Italy
2 RWTH Aachen University, Institut für Mathematik, RTG Energy, Entropy, and Dissipative Dynamics, Templergraben 55 (111810), 52062 Aachen, Germany
* Corresponding author: firstname.lastname@example.org
Accepted: 23 March 2023
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.
Mathematics Subject Classification: 35B25 / 93E20 / 93C70 / 49L25
Key words: Singular perturbations / two-scale systems / stochastic optimal control / homogenization / viscosity solutions / Hamilton-Jacobi-Bellman equations / invariant measures
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.