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2022 Backward propagation of chaos
Mathieu Laurière, Ludovic Tangpi
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Electron. J. Probab. 27: 1-30 (2022). DOI: 10.1214/22-EJP777

Abstract

This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic differential equations. Under standard assumptions on the coefficients of the equations, we prove propagation of chaos results and quantitative estimates on the rate of convergence in Wasserstein distance of the empirical measure of the interacting system to the law of a McKean-Vlasov type equation. These results are accompanied by non-asymptotic concentration inequalities. As an application, we derive rate of convergence results for solutions of second order semilinear partial differential equations to the solution of a partial differential written on an infinite dimensional space.

Funding Statement

The work of M. Laurière was supported by ARO grant AWD1005491 and NSF award AWD1005433. The work of L. Tangpi was supported by NSF grant DMS-2005832.

Citation

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Mathieu Laurière. Ludovic Tangpi. "Backward propagation of chaos." Electron. J. Probab. 27 1 - 30, 2022. https://doi.org/10.1214/22-EJP777

Information

Received: 14 June 2020; Accepted: 3 April 2022; Published: 2022
First available in Project Euclid: 6 June 2022

Digital Object Identifier: 10.1214/22-EJP777

Subjects:
Primary: 28C20 , 35B40 , 35K58 , 60F25 , 60H20 , 60J60

Keywords: BSDE , concentration of measure , interacting particles systems , McKean-Vlasov BSDE , PDEs on Wasserstein space , propagation of chaos

JOURNAL ARTICLE
30 PAGES


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Vol.27 • 2022
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