From the 2 of 5 linked papers with an AI index.
5 papers
Modelling Anomalous Diffusion: The Role of CTRWs and Non-Local Dynamics
Ivan BioÄiÄ, Bruno Toaldo
The paper surveys the stochastic framework for anomalous diffusion using continuous-time random walks (CTRWs), their scaling limits, and the resulting non‑local (fractional‑type) e…
Time-changed Markov processes and space-time coupled non-local equations
Giacomo Ascione, Enrico Scalas, Bruno Toaldo +1
The paper develops a theory for coupled space‑time non‑local equations, proving existence, uniqueness and a maximum principle, and represents solutions via time‑changed stochastic…
Non-local heat equations with moving boundary
Giacomo Ascione, Pierre Patie, Bruno Toaldo
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for…
Random Flights and Anomalous Diffusion: A Non-Markovian Take on Lorentz Processes
Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas +1
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Galla…
Para-Markov chains and related non-local equations
Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas +1
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 def…