On aggregation of multitype Galton–Watson branching processes with immigration
Mátyás BarczyMTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Aradi vrtank tere 1, H-6720 Szeged, HungaryFanni K. NedényiBolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, HungaryGyula PapBolyai Institute, University of Szeged, Aradi vrtank tere 1, H-6720 Szeged, Hungary
2018en
ABI
Аннотация
Limit behaviour of temporal and contemporaneous aggregations of independent copies of a stationary multitype Galton–Watson branching process with immigration is studied in the so-called iterated and simultaneous cases, respectively. In both cases, the limit process is a zero mean Brownian motion with the same covariance function under third order moment conditions on the branching and immigration distributions. We specialize our results for generalized integer-valued autoregressive processes and single-type Galton–Watson processes with immigration as well.
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