SOME PECULIAR SEMI-MARKOV PROCESSES
Walter L. Smith · 1967
Experience with semi-Markov processes with finite expected waits suggests that the behavior of Markov processes is a good guide to understanding the behavior of the more general process.However, examples are given to show that when expected waits are infinite quite surprising behavior is possible.For a two-state aperiodic semi-Markov process the instantaneous state probabilities Pi(t) can have (C, l)-limits but not strict limits; for a three-state (and irreducible) process one can have Po(t) tend to a strict limit as t -oo but Pi(t) and P2(t) not even have (C, l)-limits.For an aperiodic irreducible infinite chain one can have Pi(t) -7ri > 0 as t -oo, for every i, yet 2: 7ri < 1.