Facciaroni Lorenzo, Ricciuti Costantino, Scalas Enrico, Toaldo Bruno
Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Rome, Italy.
Dipartimento di Matematica "Giuseppe Peano", Università degli studi di Torino, Turin, Italy.
Fract Calc Appl Anal. 2025;28(3):1071-1093. doi: 10.1007/s13540-025-00390-9. Epub 2025 Apr 2.
There is a well-established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times, although marginally Mittag-Leffler, are assumed to be stochastically dependent. This creates a long memory tail in the evolution, unlike what happens for semi-Markov processes. As a special case of these chains, we study a particular counting process which extends the well-known fractional Poisson process, the last one having independent, Mittag-Leffler waiting times.
有一个成熟的理论将具有米塔格 - 莱夫勒等待时间的半马尔可夫链与时间分数方程联系起来。我们在此超越半马尔可夫框架，通过定义一些非马尔可夫链，其等待时间虽然略微呈米塔格 - 莱夫勒分布，但被假定为随机相关。这在演化过程中产生了一个长记忆尾，这与半马尔可夫过程的情况不同。作为这些链的一个特殊情况，我们研究一个特定的计数过程，它扩展了著名的分数泊松过程，后者具有独立的米塔格 - 莱夫勒等待时间。
