Author

Shao-Lin Ji

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Preprint Sep 2026

Variable-Coefficient Parabolic Equations and Finite-Horizon Hamilton--Jacobi--Bellman Equations in Augmented Spectral Barron Spaces

We establish a whole-space solution framework in augmented spectral Barron spaces for uniformly elliptic parabolic equations with state-dependent principal coefficients. A frozen-symbol parametrix yields bounded Green and terminal operators and a one-derivative smoothing estimate on arbitrary finite horizons, without r...

Shao-Lin Ji, Xian-Rui Wang · 1 citation

#machine learning Preprint Sep 2026

Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support

Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely treats ambient-space regularity or data supported exactly on low-dimensional sets. We study linear FM under a noisy latent-generator model, where a low-dimensional H\"older...

Li-Feng Hao, Shao-Lin Ji · 0 citations

Preprint Sep 2026

Finite-Horizon Hamilton--Jacobi--Bellman Equations with State-Dependent Diffusion in Spectral Barron Spaces

We study high-dimensional finite-horizon Hamilton--Jacobi--Bellman equations for controlled diffusions with uniformly elliptic, state-dependent diffusion coefficients. Motivated by the need for a rigorous analytical framework that explains neural-network approximation in high-dimensional stochastic control, we formulat...

Shao-Lin Ji, Xian-Rui Wang · 0 citations