On the limit distributions for partially observed branching processes with generation-dependent detection

© ISOSS Publications 2015. In the paper we consider the following modification of a discrete time branching process. In each generation a binomially distributed subset of the population will be observed. The probability for each individual to be observed depends on the number of the generation to which it belongs. The number of observed individuals constitute a partially observed branching process. After inspection both observed and unobserved individuals may change their offspring distributions. This makes the process after inspection to evolve in a varying environment. We derive limiting distributions for the vector of the inspected and partially observed branching processes in cases when the inspected processes in the varying environment are counterparts of subcritical, critical and supercritical processes