Backward propagation of chaos

Mathieu Laurière, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number69
JournalElectronic Journal of Probability
Volume27
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

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

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