Population processes sampled at random times

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are investigated. In particular, we study the hitting times in all cases and examine their long-range behavior. The time-changed population models considered here display upward (Birth process) and downward jumps (death processes) of arbitrary size and, for this reason, can be adopted as adequate models in ecology, epidemics and finance situations, under stress conditions.