Harmonic problems arising from continuous time random walks limit processes
Abstract
In this paper, we develop a universal method that identifies the (non-local) governing evolution equations for Continuous Time Random Walks' (CTRWs) limit processes. Given one of these processes, our method provides the form of a non-local operator, acting on space and time variables jointly, such that the (generalized) harmonic problem associated with it represents an evolution governing equation for this process. Then, the well-posedness of this problem must be established case by case. In this paper, we establish well-posedness when the process is a Feller process (on a general Polish space ) time-changed with the overshooting of a subordinator. Also, we will show how our method applies to several cases when the equation and its well-posedness are already known, hence unifying several different approaches in the literature.
Cite
@article{arxiv.2505.14550,
title = {Harmonic problems arising from continuous time random walks limit processes},
author = {Ivan Biočić and Bruno Toaldo},
journal= {arXiv preprint arXiv:2505.14550},
year = {2025}
}