Piecewise Birth-Death Processes
2002, v.8, Issue 4, 665-698
A natural generalization of the ordinary birth-death processes, the Piecewise Birth-Death Process is considered. The close relationship between this kind of processes and the well-known ordinary birth-death processes is revealed. Regularity criteria for such processes are established. Properties of such structure are further presented. In particular, conditions for recurrence and positive recurrence are obtained. Equilibrium distributions are given for the ergodic case. Some useful properties of the transient Piecewise Birth-Death process are also provided. Probabilistic meanings of the analytic results are explained. These results are then illustrated through several examples.
Keywords: birth-death processes,piecewise birth-deathprocesses,uniqueness,recurrence,positive recurrence,equilibrium distributions,regularity,Feller minimal processes