Poisson计数过程的绝对正则性和遍历性
Absolute regularity and ergodicity of Poisson count processes
摘要：
我们考虑一类观测驱动的泊松计数过程，其中伴随的强度过程的当前值取决于两个过程的先前值。在压缩条件下，我们证明了二元过程具有唯一的平稳分布，并且计数过程的平稳版本是绝对正则的。此外，由于强度可以写为计数变量的可测泛函，我们得出结论，二元过程是遍历的。作为这些结果的一个重要应用，我们展示了如何测试方法以前使用的独立的泊松数据的情况下，可以使用的情况下，泊松计数过程。
英文摘要：
We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that a stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables, we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.
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