In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence property. It is proved by establishing an asymptotic result for the covariance of inverse mixed stable subordinator. Also, it is shown that the increment process of the MFPP, namely the mixed fractional Poissonian noise, has the short-range dependence property.

中文翻译：

---

关于混合分数泊松过程的长程相关性

在本文中，我们展示了混合分数泊松过程 (MFPP) 表现出长程相关性。通过建立逆混合稳定从属项的协方差的渐近结果证明了这一点。同时，表明MFPP的增量过程，即混合分数泊松噪声，具有短程相关性。