Limit theorems in critical Galton-Watson branching processes with migration

Abstract

We study critical Galton-Watson branching processes with migration. It is assumed that the second moment of the number of direct descendants is infinite. Limit theorems are proved for the case where the mean value of migration is equal to zero. The work generalizes the results obtained by Nagaev and Khan [Teor. Veroyatn. Ee Primen.,25, No. 3, 523–534 (1980)] for the case where the second moment is finite.