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Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space

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arxiv 2408.06013 v2 pith:QEGZX3OS submitted 2024-08-12 math.AP

Erhan Bayraktar , Ibrahim Ekren , Xin Zhang This is my paper · ORCID
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keywords pdesspacewassersteinconvergencerateparticlesecond-ordervalue
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In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dimensional inf(sup)-convolution of the finite-dimensional value function yields a super (sub)-viscosity solution to the PDEs on Wasserstein space. Hence, we obtain a convergence rate using a comparison principle of such PDEs on Wasserstein space. Our argument is purely analytic and relies on the regularity of value functions established in \cite{DaJaSe23}.

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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. A particle system approach towards the global well-posedness of master equations for potential mean field games of control

    math.OC 2024-12 conditional novelty 6.0 of 10

    Under an extended displacement convexity condition, classical solutions to the HJB and master equations for generalized mean field control and potential mean field games of controls exist globally, including in the de...

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