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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
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space

    math.OC 2025-01 conditional novelty 7.0 of 10

    The value function of mean field control with common noise is the unique viscosity solution of a fully second-order HJB equation in the Wasserstein space.

  2. The randomization method in stochastic optimal control

    math.OC 2025-02 conditional novelty 1.0 of 10

    A survey of the randomization method proving that the value of an optimal control problem equals the value of a randomized problem and is represented by a constrained BSDE, with a complete tour of applications.

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