On total progeny of multitype Galton-Watson process and the first   passage time of random walk with bounded jumps
  In this paper, we first form a method to calculate the probability generating function of the total progeny of multitype branching process. As examples, we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and (2-1) random walk. Consequently, we could give the probability generating functions and the distributions of the hitting time of corresponding random walks. 
Wang Huaming
math.PR