On multitype processes based on progeny length of particles of a supercritical Galton-Watson process

Abstract

Based on infinite and finite line of descent of particles of a one-dimensional supercritical Galton-Watson branching process (GWBP), we construct an associated bivariate process. We show that this bivariate process is a two-dimensional, supercritical GWBP. We also show that this process retains its branching property on appropriate probability spaces, when conditioned on set of non-extinction and set of extinction. Some asymptotic and weak convergence results for this process have been established. A generalisation of these results to a multitype p-dimensional GWBP has also been carried out.