LONG-TERM BEHAVIOR OF SURVIVAL CHANCES IN SUBCRITICAL GALTON-WATSON PROCESSES WITH DISCRETE TIME

In this paper, Kolmogorov's famous theorem is generalized to the subcritical case, known from the discrete-time subcritical Galton-Watson branching processes theory. In this theorem, the Kolmogorov constant for the subcritical state is defined, and its exact form is determined. The results highlighted several important classical results in the subcritical random branching processes theory. In particular, using our results, local limit theorems are derived for subcritical random branching theories.