It is well known that the set of non-negative integers is the state-space of usual branching stochastic processes. However in many applications one may have situations when it is difficult to count the number of individuals in the population, but some non-negative characteristic, such as volume,...

The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with nonhomogeneous immigration is established, under moment assumptions on both reproduction and immigration. The proofs use martingale techniques and weak convergence...