论文标题
复杂的分数泊松过程
Convoluted Fractional Poisson Process
论文作者
论文摘要
在本文中，我们通过在控制其状态概率的分数微分方程系统中对空间变量进行离散卷积，介绍和研究时间分数泊松过程的复杂版本。我们将引入的过程称为复杂的分数泊松过程（CFPP）。获得其状态概率的拉普拉斯变换的显式表达，其反演产生其一维分布。获得了一些统计属性，例如概率生成函数，力矩生成功能，力矩等。研究了CFPP的特殊情况，即，研究了复杂的泊松过程（CPP），并讨论了其与CFPP的时间变化的从属关系。结果表明，CPP是使用CFPP的远程依赖性属性的Lévy过程。此外，我们表明CFPP的增量表现出短程依赖性属性。
In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking the discrete convolution with respect to space variable in the system of fractional differential equations that governs its state probabilities. We call the introduced process as the convoluted fractional Poisson process (CFPP). The explicit expression for the Laplace transform of its state probabilities are obtained whose inversion yields its one-dimensional distribution. Some of its statistical properties such as probability generating function, moment generating function, moments etc. are obtained. A special case of CFPP, namely, the convoluted Poisson process (CPP) is studied and its time-changed subordination relationships with CFPP are discussed. It is shown that the CPP is a Lévy process using which the long-range dependence property of CFPP is established. Moreover, we show that the increments of CFPP exhibits short-range dependence property.
