On a robust version of the integral representation formula of nonlinear filtering
On a robust version of the integral representation formula of nonlinear filtering
复制标题
非线性滤波积分表示公式的鲁棒版本
DOI：
10.1007/s00440-004-0412-5
复制
发表时间：
2005
影响因子：
2
通讯作者：
D. Crisan
中科院分区：
文献类型：
--
作者：
J.M.C. Clark;D. Crisan
摘要。研究了非线性滤波条件期望算子的鲁棒表示公式，讨论了如何完成“未完成的业务”。这样一个公式是稳健的，因为它对观测过程的依赖是连续的，在[2]中没有证明。本文的主要目的就是弥补这一不足。这个公式“几乎是显而易见的”，因为它可以在形式层面上通过应用于积分表示公式中出现的随机积分的分部积分过程推导出来。然而，这个公式的严格论证是相当微妙的，因为它依赖于一个可测量性论证，而这个论证的必要性乍一看很容易被忽略。对于一类扩散，Kushner[9]证明了表示的连续性（但不是有效性）。
Abstract.The paper is concerned with completing “unfinished business” on a robust representation formula for the conditional expectation operator of nonlinear filtering. Such a formula, robust in the sense that its dependence on the process of observations is continuous, was stated in [2] without proof. The main purpose of this paper is to repair this deficiency.The formula is “almost obvious” as it can be derived at a formal level by a process of integration-by-parts applied to the stochastic integrals that appear in the integral representation formula. However, the rigorous justification of the formula is quite subtle, as it hinges on a measurability argument the necessity of which is easy to miss at first glance. The continuity of the representation (but not its validity) was proved by Kushner [9] for a class of diffusions.