TITLE:
An Infinite Series Expression for the Joint Probability Density Function of OccupationTimes in a Three-State Markov Chain
AUTHORS:
James Evans, Andrzej Korzeniowski
KEYWORDS:
Occupation Times, Markov Chains, Moment Generating Functions, Probability Density Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.11,
November
18,
2025
ABSTRACT: We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we demonstrate that Pedler’s technique of employing moment generating functions can be applied to the three-state case as well.