The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively applies the ensemble Kalman update to evolve (the approximation of the) prior into the posterior measure. For the convergence analysis of the EKI it is common practice to derive a continuous version, replacing the iteration with a stochastic differential equation. In this paper we validate this approach by showing that the stochastic EKI iteration converges to paths of the continuous-time stochastic differential equation by considering both the nonlinear and linear setting, and we prove convergence in probability for the former, and convergence in moments for the latter. The methods employed can also be applied to the analysis of more general numerical schemes for stochastic differential equations in general.

翻译：合成Kalman反转法(EKI)是估计(拜耶斯)反倒问题背景下未知参数的一种方法。该方法以粒子共集相近基本测量法,并迭接地应用共合Kalman更新法,在后继测量法中先演化(近似值)。对于EKI的趋同分析,通常的做法是得出一个连续版本,用随机差分方程取代迭代。在本文中,我们验证了这一方法,通过考虑到非线性和线性设置,表明随机EKI迭代法与连续时间随机差异方程的路径汇合,我们证明前者的概率趋同,后者的瞬间趋同。所采用的方法也可以用于分析一般的随机差异方程的更一般性数字方案。