Asymptotics of nearly critical Galton-Watson processes with immigration
Tóm tắt
We investigate the inhomogeneous Galton-Watson processes with immigration, where πn, the offspring means in the nth generation, tends to 1. We show that if the second derivatives of the offspring generating functions go to 0 rapidly enough, then the asymptotics are the same as in the INAR(1) case, treated in [4]. We also determine the limit if this assumption does not hold showing the optimality of the conditions.
Tài liệu tham khảo
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