Fluctuation limits of multitype branching random fields

A system of particles of k types with immigration in Rd is considered. Each particle, according to its type, independently migrates following a symmetric stable process, lives an exponential amount of time and produces particles of all the types. The asymptotic behavior of the vector measure valued process difined by the system is studied for three different rescalings. The results are laws of large numbers, functional central limit theorems, and properties of the generalized fluctuation limit processes (continuity, Langevin equations, large time behavior, spectral measures). These results include the known ones for the single type case.