A note on the state occupancy distribution for Markov chains

2025/03/22 by Pollett, Phil
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.17647

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.

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