Extinction Probabilities in Branching Processes

Abstract

Denote by Z _n the size of the nth generation, and by P _n the generating function of its probability distribution. By assumption Z₀ = 1 and

$$P_1 (s) = P(s) = \sum\limits_{k = 0}^\infty {P_k s^k.} $$

(4.1)

From An Introduction to Probability Theory and its Applications, Volume 1, third edition (revised printing), pages 295–298. New York : John Wiley & Sons.