论文标题
非线性过滤器连续性弱条件
Equivalent Conditions for Weak Continuity of Nonlinear Filters
论文作者
论文摘要
本文研究了非线性过滤器的连续性弱。众所周知，当原始离散时间过程被其状态是信念概率的过程所取代时，可以保留过渡概率的Borel过渡概率的可测量性。众所周知，类似的保存可能不适合过渡概率的弱连续性。在本文中，我们表明，Kara，Saldi和Yuksel（2019）引入的信念的过渡概率的连续性较弱的足够条件是半均匀的过渡概率连续性的必要和足够条件。在Feinberg，Kasyanov和Zgurovsky（2021）中引入了半均匀的候选者连续性的性质，如果原始过渡概率具有此特性，则该过程的过渡概率，其状态是由信仰概率和观察的一对，也具有该特性。因此，该属性意味着非线性过滤器的连续性较弱。本文还审查了半均匀的候车者连续性的几个必要和足够的条件。
This paper studies weak continuity of nonlinear filters. It is well-known that Borel measurability of transition probabilities for problems with incomplete state observations is preserved when the original discrete-time process is replaced with the process whose states are belief probabilities. It is also known that the similar preservation may not hold for weak continuity of transition probabilities. In this paper we show that the sufficient condition for weak continuity of transition probabilities for beliefs introduced by Kara, Saldi, and Yuksel (2019) is a necessary and sufficient condition for semi-uniform Feller continuity of transition probabilities. The property of semi-uniform Feller continuity was introduced in Feinberg, Kasyanov, and Zgurovsky (2021), and, if the original transition probability has this property, then the transition probability of the process, whose state is a pair consisting of the belief probability and observation, also has this property. Thus, this property implies weak continuity of nonlinear filters. This paper also reviews several necessary and sufficient conditions for semi-uniform Feller continuity.
