论文标题
离散观察到的相互作用粒子系统的参数估计
Parameter estimation of discretely observed interacting particle systems
论文作者
论文摘要
在本文中，我们考虑了随机McKean-Vlasov方程的漂移和扩散系数的关节参数估计问题以及相关的相互作用粒子系统。分析在一般框架中提供，因为两个系数都取决于过程的解和解决方案本身的定律。从对固定间隔$ [0，t] $的离散观察开始，我们提出了基于伪可能方法方法的对比函数。我们表明，当离散化步骤（$δ_n$）和颗粒数（$ n $）满足$Δ_N\ rightArrow 0 $和$ n \ rightArrow \ infty $时，相关的估计器是一致的，而当条件$Δ_nn \ rightarrow 0 $ holds时。
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution of the process and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval $[0, T]$, we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step ($Δ_n$) and the number of particles ($N$) satisfy $Δ_n \rightarrow 0$ and $N \rightarrow \infty$, and asymptotically normal when additionally the condition $Δ_n N \rightarrow 0$ holds.
