CONVERGENCE RATE OF PARTICLE SYSTEM FOR SECOND-ORDER PDES ON WASSERSTEIN SPACE

Erhan Bayraktar; Ibrahim Ekren; Xin Zhang

doi:10.1137/23M1625482

CONVERGENCE RATE OF PARTICLE SYSTEM FOR SECOND-ORDER PDES ON WASSERSTEIN SPACE

Erhan Bayraktar, Ibrahim Ekren, Xin Zhang

Finance and Risk Engineering

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Abstract

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 [S. Daudin, J. Jackson, and B. Seeger, Commun. Partial Differential Equations, 50 (2025), pp. 1-52].

Original language	English (US)
Pages (from-to)	1768-1782
Number of pages	15
Journal	SIAM Journal on Control and Optimization
Volume	63
Issue number	3
DOIs	https://doi.org/10.1137/23M1625482
State	Published - 2025

Keywords

comparison principle
second-order PDEs
viscosity solutions
Wasserstein space

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/23M1625482

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title = "CONVERGENCE RATE OF PARTICLE SYSTEM FOR SECOND-ORDER PDES ON WASSERSTEIN SPACE",

abstract = "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 [S. Daudin, J. Jackson, and B. Seeger, Commun. Partial Differential Equations, 50 (2025), pp. 1-52].",

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T1 - CONVERGENCE RATE OF PARTICLE SYSTEM FOR SECOND-ORDER PDES ON WASSERSTEIN SPACE

AU - Bayraktar, Erhan

AU - Ekren, Ibrahim

AU - Zhang, Xin

PY - 2025

Y1 - 2025

N2 - 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 [S. Daudin, J. Jackson, and B. Seeger, Commun. Partial Differential Equations, 50 (2025), pp. 1-52].

AB - 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 [S. Daudin, J. Jackson, and B. Seeger, Commun. Partial Differential Equations, 50 (2025), pp. 1-52].

KW - comparison principle

KW - second-order PDEs

KW - viscosity solutions

KW - Wasserstein space

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CONVERGENCE RATE OF PARTICLE SYSTEM FOR SECOND-ORDER PDES ON WASSERSTEIN SPACE

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Keywords

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