论文标题
一类部分观察到的扩散的无偏过滤
Unbiased Filtering of a Class of Partially Observed Diffusions
论文作者
论文摘要
在本文中，我们考虑了一种基于蒙特卡洛的方法，可以过滤在常规和离散时间观察到的部分观察到的扩散。仅访问扩散过程的Euler离散化，我们提出了一个新的过程，该过程可以返回对过滤分布的在线估计，而无需离散化偏差和有限的差异。我们的方法基于Rhee＆Glynn（2015）随机方法的新型双重应用以及Jasra等人（2017）的多级粒子滤波器（MLPF）方法。在单个处理器上，我们的新方法与MLPF的数值比较表明，相似的误差可能会导致计算成本的轻度增加。但是，新方法大大扩展到任意许多处理器。
In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee & Glynn (2015) along with the multilevel particle filter (MLPF) approach of Jasra et al (2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.
