9 papers
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…
Quantitative Particle Approximation for Controlled Nonlinear Filtering
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We estimate convergence rates of value functions for particle approximations of a controlled nonlinear filtering problem. The state is a McKean--Vlasov diffusion on the flat torus,…
A comparison principle for Wasserstein PDEs with state- and law-dependent common noise
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We prove a comparison principle for a class of second-order Hamilton--Jacobi--Bellman equations on the Wasserstein space whose second-order term is generated by a general common-no…
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…