This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the scenario where both the time horizon $T$ and the number of particles $N$ tend to infinity. Our proposed method recovers polynomial rates of convergence for the resulting estimator. This is achieved under the assumption of exponentially decaying tails for the interaction function. Additionally, we conduct a thorough analysis of the transform of the associated invariant density as a complex function, providing essential insights for our main results.

翻译：本文研究一类McKean-Vlasov随机微分方程中交互函数的估计问题。该估计基于关联粒子系统在时间$T$处的观测，考虑时间跨度$T$与粒子数$N$同时趋于无穷的场景。我们提出的方法恢复了所得估计量的多项式收敛速率，这是在交互函数具有指数衰减尾部假设下实现的。此外，我们对关联不变密度作为复函数的变换进行了深入分析，为主要结果提供了关键见解。