论文标题
具有可预测的跳跃和路径依赖性局部特征的纯跳跃过程的随机过滤
Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics
论文作者
论文摘要
本文的目的是研究部分可观察过程$（x，y）$的系统的过滤问题，其中$ x $是代表信号的非马克维亚纯跳跃过程，$ y $是一般的跳跃扩散，可提供观察。我们的模型涵盖了这两个过程不一定是准左连续的情况，从而使它们可以在可预测的停止时间跳跃。通过介绍信号的马尔可夫版本，我们可以通过创新方法计算过滤过程的显式方程。
The objective of this paper is to study the filtering problem for a system of partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump process representing the signal and $Y$ is a general jump-diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filtering process via the innovations approach.
