Sequential Propagation of Chaos for Mean-Field BSDE Systems

A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations. It is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles grows. Based on the Wasserstein metric, quantitative propagation of chaos results are obtained for both linear and quadratic growth conditions. Finally, numerical experiments are conducted to validate our theoretical results.