Solution Theory of Hamilton–Jacobi–Bellman Equations in Spectral Barron Spaces
Abstract
Abstract. We study the solution theory of the whole-space static (elliptic) Hamilton–Jacobi–Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the discount factor is sufficiently large, there exists a sequence of uniformly bounded spectral Barron functions that converges locally uniformly to the solution. As a consequence, the solution of the HJB equation can be approximated by two-layer neural networks without curse of dimensionality.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Spectral Theory in Mathematical Physics
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 1
- Pages
- 636–660
- Publication date
- 17 February 2026
- Language
- EN