We consider birth–death processes on the nonnegative integers, where {1,2,…} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional...

Conditions are obtained for the truncated birth-death process to be stochastically monotone in the long run.