Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space
Abstract
In this paper, we prove a comparison result for semi-continuous viscosity solutions of a class of second-order PDEs in the Wasserstein space. This allows us to remove the Lipschitz continuity assumption with respect to the Fourier-Wasserstein distance in AriX: 2309.05040 and obtain uniqueness by directly working in the Wasserstein space. In terms of its application, we characterize the value function of a stochastic control problem with partial observation as the unique viscosity solution to its corresponding HJB equation. Additionally, we present an application to a prediction problem under partial monitoring, where we establish an upper bound on the limit of regret using our comparison principle for degenerate dynamics.
Cite
@article{arxiv.2504.18697,
title = {Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space},
author = {Erhan Bayraktar and Ibrahim Ekren and Xihao He and Xin Zhang},
journal= {arXiv preprint arXiv:2504.18697},
year = {2025}
}
Comments
To appear in the Journal of Differential Equations. Keywords: Wasserstein space, second-order PDEs, viscosity solutions, comparison principle