Quasi-stationary distributions have been used in biology to describe the steady state behaviour of Markovian population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. However, they have substantial drawbacks; a...

For S a subordinator and [Pi]n an independent Poisson process of intensity we are interested in the number Kn of gaps in the range of S that are hit by at least one point of [Pi]n. Extending previous studies in [A.V. Gnedin, The Bernoulli sieve, Bernoulli 10 (2004) 79-96; A.V. Gnedin, J. Pitman,...