6 papers · 1 filter
Sharp Wasserstein Convergence Rates for Empirical Path Laws of Itô Processes
Xihao He, Fengyi Yuan
We establish the sharp logarithmic order for the expected -Wasserstein distance, induced by the supremum norm, between the empirical law of independent cop…
Mean-field games with rough common noise: the compactification approach
Erhan Bayraktar, Xihao He, Xiang Yu +1
We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driv…
Comparison of viscosity solutions for a class of non-linear PDEs on the space of finite nonnegative measures
Ibrahim Ekren, Xihao He, Tianxu Lan +1
We establish a comparison principle for viscosity solutions of a class of nonlinear partial differential equations posed on the space of nonnegative finite measures, thereby extend…
Graphon particle systems with common noise
Erhan Bayraktar, Xihao He, Donghan Kim
We study a nonlinear graphon particle system driven by both idiosyncratic and common noise, where interactions are governed by a graphon and represented as positive finite measures…
A mean-field version of Bank-El Karoui's representation of stochastic processes
Xihao He, Xiaolu Tan, Jun Zou
We study a mean-field version of Bank-El Karoui's representation theorem of stochastic processes. Under different technical conditions, we establish some existence and uniqueness r…
On the limit theory of mean field optimal stopping with non-Markov dynamics and common noise
Xihao He
This paper focuses on a mean-field optimal stopping problem with non-Markov dynamics and common noise, inspired by Talbi, Touzi, and Zhang \cite{TalbiTouziZhang1,TalbiTouziZhang3}.…