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.
Quantitative Convergence for Mean Field Control with Common Noise and Degenerate Idiosyncratic Noise.arXiv preprint arXiv:2409.14053, 2024
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A comparison principle for viscosity solutions of nonlinear PDEs on finite nonnegative measures is proved and used to characterize the value function of a controlled branching McKean-Vlasov diffusion as the unique viscosity solution of the associated HJB equation.
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Comparison of viscosity solutions for a class of non-linear PDEs on the space of finite nonnegative measures
A comparison principle for viscosity solutions of nonlinear PDEs on finite nonnegative measures is proved and used to characterize the value function of a controlled branching McKean-Vlasov diffusion as the unique viscosity solution of the associated HJB equation.