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arXiv · 2309.05040

Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space

Erhan Bayraktar·Ibrahim Ekren·Xin Zhang
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Abstract

We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma, which is tailor-made for the class of equations we consider.

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Erhan Bayraktar, Ibrahim Ekren, Xin Zhang. 2023-09-10. Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space. https://arxiv.org/abs/2309.05040

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