THE STRUCTURE OF DECOMPOSABLE REDUCED BRANCHING PROCESSES. II. FUNCTIONAL LIMIT THEOREMS

摘要

A decomposable strongly critical Galton-Watson branching process, with N types of particles labeled 1, 2,..., N, is considered in which particles of type i may produce offspring of types j >= i only. Functional limit theorems are proved describing the structure of the reduced process generated by the initial one, and the distributions of the birth moment and the type of the most recent ancestor of all particles existing in the population at a distant moment n are found.