论文标题
一种用于相互作用粒子系统及其平均场极限的矩估计器的方法
A method of moments estimator for interacting particle systems and their mean field limit
论文作者
论文摘要
我们研究了从系统中一个单个粒子的路径中学习与多项式漂移，相互作用和扩散函数的随机相互作用粒子系统中未知参数的问题。我们的估计器是通过求解线性系统来获得的，该系统是通过在平均场极限的不变分布和该过程的二次变化上施加适当条件来构建的。我们的方法很容易实现，因为它仅需要通过厄贡定理和低维线性系统的解决方案近似。此外，我们证明我们的估计量在无限数据和无限数量粒子的极限上是渐进的（平均场极限）。此外，我们提出了几个数值实验，这些实验验证了理论分析，并显示了我们方法学对相互作用粒子系统中准确推断参数的有效性。
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear system which is constructed by imposing appropriate conditions on the moments of the invariant distribution of the mean field limit and on the quadratic variation of the process. Our approach is easy to implement as it only requires the approximation of the moments via the ergodic theorem and the solution of a low-dimensional linear system. Moreover, we prove that our estimator is asymptotically unbiased in the limits of infinite data and infinite number of particles (mean field limit). In addition, we present several numerical experiments that validate the theoretical analysis and show the effectiveness of our methodology to accurately infer parameters in systems of interacting particles.
