Abstract

In this paper, we introduce and study a time-changed version of the space-time fractional Poisson process (STFPP) by time changing it by an independent Lévy subordinator with finite moments of any order. We call the introduced process as the time-changed fractional Poisson process (TCFPP). The probability mass function, probability generating function and a variant of the law of iterated logarithm for the TCFPP are obtained. Several special cases of the TCFPP are considered and their governing differential equations are derived. Later, we consider the STFPP time-changed by inverse of Lévy subordinator and discuss its particular cases.

中文翻译：

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时变时空分数泊松过程

摘要

在本文中，我们介绍并研究了时空分数泊松过程（STFPP）的时变版本，方法是由独立的Lévy从属对任意阶次有限矩进行时间更改。我们将引入的过程称为时变分数泊松过程（TCFPP）。获得了TCFPP的概率质量函数，概率生成函数和迭代对数律的变体。考虑了TCFPP的几种特殊情况，并推导了它们的控制微分方程。稍后，我们考虑STFPP被Lévy下级从属逆时变，并讨论其特殊情况。