The multitype branching random walk: Temporal and spatial limit theorems

The paper considers a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, n⇒• is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.