论文标题
对Zakai方程解决方案的无偏估计
Unbiased Estimation of the Solution to Zakai's Equation
论文作者
论文摘要
在接下来的文章中，我们考虑了连续时间的非线性过滤问题，尤其是对Zakai方程或归一化常数的解决方案。我们开发了一种产生有限差异的方法，几乎肯定是对Zakai方程解决方案的无偏估计量。也就是说，仅访问Zakai方程解决方案的一阶离散化，我们提出了一种可以消除此离散化偏置的方法。在假设下，该方法已被证明具有有限的方差，并且在数值上与使用特定的多级蒙特卡洛方法进行了比较。
In the following article we consider the non-linear filtering problem in continuous-time and in particular the solution to Zakai's equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai's equation. That is, given access to only a first order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.
