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math.PR2026
Optimal Weighted Hessian Estimates for Parabolic Equations under General Diffusion Marginals
Jihao Long, Zhenhua Zhao
We study weighted Hessian estimates for parabolic terminal equations under the marginals of a prescribed diffusion, allowing singular initial laws and different principal coe…
math.PR2021
A Class of Dimension-free Metrics for the Convergence of Empirical Measures
Jiequn Han, Ruimeng Hu, Jihao Long
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is fre…
math.PR2018★ 139 cited
Convergence of the Deep BSDE Method for Coupled FBSDEs
Jiequn Han, Jihao Long
The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs…