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## Pap Gyula (SZTE): Almost sure, L1- and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration

 Szerda, 14. Március 2018, 14:00 - 16:00
Abstract. Under a first order moment condition on the immigration mechanism, we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration (CBI process) converges almost surely. If an x*log(x) moment condition on the branching mechanism does not hold, then the limit is zero. If this x*log(x) moment condition holds, then we prove L1 convergence as well. The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing. If, in addition, a suitable extra power moment condition on the branching mechanism holds, we provide the correct scaling for the projection of a CBI process on certain left eigenvectors of the branching mean matrix in order to have almost sure and L1 limit. Moreover, under a second moment condition on the branching and immigration mechanisms, we prove L2 convergence as well. A representation of the limits is also provided. (Joint work with Mátyás Barczy and Sandra Palau.)
Hely : Szeged, Aradi vértanúk tere 1., Riesz terem.