论文标题
用于多个具有粗粒相关噪声的多个时间尺度非线性系统的过滤溶液的定量收敛性
Quantitative Convergence of the Filter Solution for Multiple Timescale Nonlinear Systems with Coarse-Grain Correlated Noise
论文作者
论文摘要
在本文中，我们证明了多个时间尺度相关的非线性系统的连续时间过滤解决方案的收敛速率，以较小的滤波方程在较大的时间尺度分离的极限下。假定相关性发生在缓慢的信号和观察过程之间。在弱拓扑中，收敛几乎是确定的。对Zakai方程解决方案的双重过程的渐近扩展，以及使用向后双随机微分方程的概率表示，以证明结果。
In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equation in the limit of large timescale separation. Correlation is assumed to occur between the slow signal and observation processes. Convergence is almost sure in the weak topology. An asymptotic expansion of the dual process for the solution to the Zakai equation, and probabilistic representation using backward doubly stochastic differential equations is leveraged to prove the result.
