Consider a semi-Markov process for which the embedded Markov chain is irreducible and positive-recurrent. Assume that the distribution of inter-renewal intervals for one state j is arithmetic with...

Consider a semi-Markov process for which the embedded Markov chain is irreducible and positive-recurrent. Assume that the distribution of inter-renewal intervals for one state j is arithmetic with span d. Show that the distribution of inter-renewal intervals for all states is arithmetic with the same span.