TITLE:
A Closed Form Probability Mass Function for Occupation Times in a Three-State Markov Chain
AUTHORS:
James Evans, Andrzej Korzeniowski
KEYWORDS:
Occupation Times, Markov Chains, Probability Generating Functions, Probability Mass Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.8,
August
28,
2025
ABSTRACT: We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a Two-State Markov chain by utilizing the method of probability generating functions given in Pedler.