Backward propagation of chaos
Backward propagation of chaos
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DOI：
10.1214/22-ejp777
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发表时间：
2019-11
影响因子：
1.4
通讯作者：
M. Laurière;Ludovic Tangpi
中科院分区：
文献类型：
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作者：
M. Laurière;Ludovic Tangpi
本文发展了一个弱相互作用粒子系统的混沌传播理论，该系统的终端位形与通常的初始位形相反，是固定的。这样的系统是由向后随机微分方程建模。在对方程系数的标准假设下，我们证明了混沌结果的传播和相互作用系统的经验测度的Wasserstein距离收敛到McKean-Vlasov型方程定律的速度的定量估计。这些结果伴随着非渐近浓度不等式。作为应用，我们得到了二阶半线性偏微分方程解到无穷维空间上的偏微分解的收敛速度.
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.