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

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arxiv 2309.05040 v3 pith:VMVCFWCD submitted 2023-09-10 math.AP math.OCmath.PR

Erhan Bayraktar , Ibrahim Ekren , Xin Zhang This is my paper · ORCID
classification math.APmath.OCmath.PR
keywords comparisonclassequationsconsidercontinuousorderproblemssecond
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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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