标题： 混沌的向后传播稳定性 显示英文标题

标题： Stability of backward propagation of chaos

摘要： 本文的目的是引入并建立关于数据集的后向传播混沌稳定性概念。例如，考虑一个离散时间鞅序列收敛到连续时间极限的情况，并且考虑一个满足后向传播混沌性质的平均场倒向随机微分方程（BSDE）系统，即收敛到一组独立同分布的McKean-Vlasov BSDE。然后，如果由离散时间鞅驱动的平均场BSDE系统收敛到由连续时间极限驱动的McKean-Vlasov BSDE序列，则我们说后向传播混沌是稳定的。我们将后向传播混沌的收敛方案视为相应数据集的像，在此基础上建立了该方案。接着，利用适当的数据集收敛概念，我们可以展示这种函数观点下的各种连续性性质。 显示英文摘要

摘要： The purpose of the present paper is to introduce and establish a notion of stability for the backward propagation of chaos, with respect to (initial) data sets. Consider, for example, a sequence of discrete-time martingales converging to a continuous-time limit, and a system of mean-field BSDEs that satisfies the backward propagation of chaos, i.e. converges to a sequence of i.i.d. McKean-Vlasov BSDEs. Then, we say that the backward propagation of chaos is stable if the system of mean-field BSDEs driven by the discrete-time martingales converges to the sequence of McKean-Vlasov BSDEs driven by the continuous-time limit. We consider the convergence scheme of the backward propagation of chaos as the image of the corresponding data set under which this scheme is established. Then, using an appropriate notion of convergence for data sets, we are able to show a variety of continuity properties for this functional point of view.