论文标题
一些复合分数泊松过程
Some Compound Fractional Poisson Processes
论文作者
论文摘要
在本文中，我们介绍和研究了三个复合泊松过程的分数版本，即钟形过程，泊松 - 陶瓷过程和广义的pólya-eaeppli工艺。结果表明，这些过程是Di Crescenzo等人最近引入过程的限制案例。 （2016年），即广义计数过程。我们为这些过程获得了平均，方差，协方差，远程依赖属性等。同样，我们获得了这些过程的分数版本的一维分布的几种等效形式。
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized Pólya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes.
