Variance estimators in critical branching processes with non-homogeneous   immigration
  The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The proofs use martingale techniques and weak convergence results in Skorokhod spaces. 
Ibrahim Rahimov and George P. Yanev
math.ST math.PR stat.TH