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arXiv · 2504.18697

Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space

Erhan Bayraktar·Ibrahim Ekren·Xihao He·Xin Zhang
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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.

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Erhan Bayraktar, Ibrahim Ekren, Xihao He, Xin Zhang. 2025-04-25. Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space. https://arxiv.org/abs/2504.18697

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