2024/12/19 by Lorenzo Facciaroni, Costantino Ricciuti, Facciaroni, Lorenzo +5 · 1 citation
Computer Science · Mathematics · #Neural Networks and Applications #Topological and Geometric Data Analysis #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2412.14979
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 our chains, we study a particular counting process which extends the well-known fractional Poisson process, the last one having independent, Mittag-Leffler waiting times.