A note on the state occupancy distribution for Markov chains
Probability
2025-04-01 v2
Abstract
In a recent paper, Shah [arXiv:2502.03073] derived an explicit expression for the distribution of occupancy times for a two-state Markov chain, using a method based on enumerating sample paths. We consider here the more general problem of finding the distribution of occupancy times for countable-state Markov chains in discrete time. Our approach, which employs generating functions, leads to arguably simpler formulae for the occupancy distribution for the two-state chain.
Keywords
Cite
@article{arxiv.2503.17647,
title = {A note on the state occupancy distribution for Markov chains},
author = {Phil Pollett},
journal= {arXiv preprint arXiv:2503.17647},
year = {2025}
}