A pure birth Markov chain is a continuous time Markov chain {Z(t):t=0} with state space S[reverse not equivalent]{0,1,2,...} such that for each i=0 the chain stays in state i for a random length of time that is exponentially distributed with mean and then jumps to (i+1). Suppose b([dot...

In a multitype (d types) supercritical positively regular Galton–Watson branching process, let {Xn,Xn−1,…,X0} denote the types of a randomly chosen (i.e., uniform distribution) individual from the nth generation and this individual’s n ancestors. It is shown here that this sequence...