Critical branching populations with reproductive sibling correlations
The classical Galton-Watson process is modified to allow the possibility that if two individuals are siblings (have a common parent in the previous generation) then their family sizes may be dependent, although retaining a constant marginal distribution. In the critical case where this distribution has mean one, analogues of the Yaglom limit laws are obtained. The technique used is to compare with the embedded process of only children, which is a critical Galton-Watson process. An extension to the general branching process is also obtained relying on results of an unpublished report by Nerman.
scientific article; zbMATH DE number 4074147