On the limit behaviour of a superadditive bisexual Galton–Watson branching process

Abstract

The asymptotic behaviour of a superadditive bisexual Galton–Watson branching process is studied. Sufficient conditions for the almost sure and L 1 convergence of the suitably normed process are given. Finally, a first approach to the study of the L 1 convergence for a superadditive bisexual Galton–Watson branching process under the Z log + Z condition is considered.