SELF-NORMALIZED LARGE DEVIATION FOR SUPERCRITICAL BRANCHING PROCESSES

We consider a supercritical branching process (Z(n), n >= 0) with offspring distribution (p(k), k >= 0) satisfying p(0) = 0 and p(1) > 0. By applying the self-normalized large deviation of Shao (1997) for independent and identically distributed random variables, we obtain the self-normalized large deviation for supercritical branching processes, which is the self-normalized version of the result obtained by Athreya (1994). The self-normalized large deviation can also be generalized to supercritical multitype branching processes.