Author

Xi-Hao He

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Preprint Aug 2026

Sharp functional quantization and empirical Wasserstein rates for It\^o processes

We establish functional quantization and empirical Wasserstein rates for continuous It\^o processes under the supremum norm. We assume that the initial condition and the drift and diffusion integrands are controlled by a time-uniform random upper bound with a finite $\rho$-moment for some $\rho>1$. Under this assumptio...

Xi-Hao He, Fengyi Yuan · 0 citations

Preprint Aug 2026

Quantitative Particle Approximation for Controlled Nonlinear Filtering

This work estimates convergence rates of value functions for particle approximations of a controlled nonlinear filtering problem and establishes uniform value-function error bounds of order under smoothness of the data, uniform ellipticity, and regularity of this Hamiltonian.

Erhan Bayraktar, Ibrahim Ekren, Xi-Hao He et al. · 0 citations

Preprint Aug 2026

Sharp Wasserstein Convergence Rates for Empirical Path Laws of It\^o Processes

We establish the sharp logarithmic order $(\log N)^{-1/2}$ for the expected $p$-Wasserstein distance, induced by the supremum norm, between the empirical law of $N$ independent copies of a continuous It\^o process and their common path law. We only assume that the initial condition and the drift and diffusion integrand...

Xi-Hao He, Fengyi Yuan · 0 citations