Fluctuation limits of multitype branching random fields (Q1190556)

This paper contains asymptotic results for a system of infinitely many particles of \(k\) different types which immigrate and diffuse in \(R^ d\), and branch according to a multitype law. Three different rescalings are considered: high density, space scaling and space-time scaling. The results are laws of large numbers, functional central limit theorems, and properties of the fluctuation limit processes, which are generalized (i.e., distribution-valued) Ornstein-Uhlenbeck processes (in particular, the generalized Langevin equations they satisfy, regularity of trajectories, large time behaviour and spectral measures). The single type case contains the known results that have been obtained by several authors (including the reviewer).