On aggregation of multitype Galton–Watson branching processes with immigration
Volume 5, Issue 1 (2018), pp. 53–79
Pub. online: 1 February 2018
Type: Research Article
Open Access
Open Access
1
Mátyás Barczy is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
Received
11 November 2017
11 November 2017
Revised
17 January 2018
17 January 2018
Accepted
18 January 2018
18 January 2018
Published
1 February 2018
1 February 2018
Abstract
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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