Parametric Estimation in Branching Processes with an Increasing Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80, 62M05The paper deals with a parametric estimation in branching processes {Zt(n)} having random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family - the class of the power series offspring distributions. Consistency and asymptotic normality of the estimators are obtained for all values of the offspring mean m, 0<m< , in the subcritical, critical and supercritical case.Partialy supported by Pro-ENBIS GTC1 -2001-43031. The paper is supported by the National Science Fund of Bulgaria, Grant No. MM-1101/2001