Author

Xian-Rui Wang

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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

Sep 2026

Age-friendly community environments and depressive symptom trajectories among middle-aged and older adults in China: Evidence from the China Health and Retirement Longitudinal Study (CHARLS).

How age-friendly community environments contribute to reducing the risk of developing adverse depressive trajectories remains an important area for scholarly inquiry. Using the China Health and Retirement Longitudinal Study (CHARLS) data from 2011 to 2020, this study employed Group-based trajectory modeling (GBTM) to i...

Xian-Rui Wang, Ting-On Chan, Fiona Fan Yang et al. · Social Science & Medicine (1... · 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