The multitype branching random walk, I

Abstract

AbstractThe limiting behaviour of the multitype branching random walk is studied. A limit theorem is proven for the supercritical process. Steady‐state distributions are shown to exist for the subcritical process with immigration, and for the critical transient process beginning with Poisson random fields. An analogue of the exponential limit law is proven for the critical process whose migration process is Brownian motion in two dimensions.