Limiting behaviour of two-level measure-branching

A measure-valued diffusion approximation to a two-level branching structure was introduced in Dawson and Hochberg (1991) where it was shown that conditioned on non-extinction at time t, and appropriately rescaled, the process converges as t . .to a non-trivial limiting distribution. Here we discuss a different approach to conditioning on non-extinction (popular in one-level branching) and relate the two limiting distributions.