论文标题
多个时间尺度，相关的非线性系统的滤波器方程的近似
Approximation of the Filter Equation for Multiple Timescale, Correlated, Nonlinear Systems
论文作者
论文摘要
本文认为，对于慢速中间过程与观察过程之间的相关性，多个时间尺度（慢速中间和快速尺度）的连续时间过滤方程的近似值。信号过程被认为是完全耦合的，将值以$ \ mathbb {r^{m}} \ times \ mathbb {r^{n}} $进行，并且没有周期性假设。事实证明，在弱拓扑中，滤波方程的解会收敛到较低尺寸平均过滤方程的溶液中，以大型时间尺度分离的极限。证明方法使用扰动的测试功能方法（校正方法）来处理中间时间尺度，以显示限制的紧密度和表征。校正器是泊松方程的解决方案。
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation process. The signal process is considered fully coupled, taking values in $\mathbb{R^{m}} \times \mathbb{R^{n}}$ and without periodicity assumptions on coefficients. It is proved that in the weak topology, the solution of the filtering equation converges in probability to a solution of a lower dimensional averaged filtering equation in the limit of large timescale separation. The method of proof uses the perturbed test function approach (method of corrector) to handle the intermediate timescale in showing tightness and characterization of limits. The correctors are solutions of Poisson equations.
