This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.
@article{arxiv.1909.04475,
title = {Variable Length Markov Chains, Persistent Random Walks: a close encounter},
author = {P. Cénac and B. Chauvin and F. Paccaut and N. Pouyanne},
journal= {arXiv preprint arXiv:1909.04475},
year = {2019}
}