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 ...

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 ...

This generating function not only yields an exact description of the distribution but also facilitates a rigorous asymptotic analysis that recovers the well-known asymptotics of the Catalan numbers ...