Full characterization of the fractional Poisson process
Full characterization of the fractional Poisson process
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分数泊松过程的完整表征
DOI：
10.1209/0295-5075/96/20004
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
E. Scalas
中科院分区：
文献类型：
--
作者：
M. Politi;T. Kaizoji;E. Scalas
分数泊松过程（FPP）是一个事件间时间独立且同分布的计数过程，遵循Mittag-Leffler分布。这一过程在应用物理和理论物理的许多领域，包括异常扩散模型中都是非常有用的。与众所周知的泊松过程相反，分数泊松过程没有平稳和独立的增量。它不是一个lsamvy过程，也不是一个Markov过程。在这封信中，我们提出了它的有限维分布函数的公式，充分表征了这一过程。这些精确的分析结果与蒙特卡罗模拟结果进行了比较。
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poisson process, the fractional Poisson process does not have stationary and independent increments. It is not a Lévy process and it is not a Markov process. In this letter, we present formulae for its finite-dimensional distribution functions, fully characterizing the process. These exact analytical results are compared to Monte Carlo simulations.