Extends Stegall's lemma to Wasserstein spaces to prove a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on probability measures over R^d.
An Approximation of the Squared Wasserstein Distance and an Application to Hamilton–Jacobi Equations.arXiv preprint arXiv:2409.11793, 2024
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Establishes the first viscosity comparison theorem for second-order PDEs on Wasserstein space with general state- and law-dependent common-noise directions via a measure-dependent Lamperti transform.
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Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces
Extends Stegall's lemma to Wasserstein spaces to prove a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on probability measures over R^d.
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A comparison principle for Wasserstein PDEs with state- and law-dependent common noise
Establishes the first viscosity comparison theorem for second-order PDEs on Wasserstein space with general state- and law-dependent common-noise directions via a measure-dependent Lamperti transform.