We present a proof showing that the weak error of a system of $n$ interacting stochastic particles approximating the solution of the McKean-Vlasov equation is $\mathcal O(n^{-1})$. Our proof is based on the Kolmogorov backward equation for the particle system and bounds on the derivatives of its solution, which we derive more generally using the variations of the stochastic particle system. The convergence rate is verified by numerical experiments, which also indicate that the assumptions made here and in the literature can be relaxed.

翻译：我们证明了逼近McKean-Vlasov方程解的$n$个相互作用随机粒子系统的弱误差为$\mathcal O(n^{-1})$。该证明基于粒子系统的Kolmogorov后向方程及其解导数的界，这些界是通过更一般地利用随机粒子系统的变分推导得出的。数值实验验证了该收敛速率，同时表明本文及现有文献中的假设条件可以进一步放宽。