Some limit theorems for the total progeny of a branching process

We consider a branching process in which each individual reproduces independently of all others and has probability a j ( j = 0, 1, · · ·) of giving rise to j progeny in the following generation. It is assumed, without further comment, that 0 < a 0 , a 0 + a 1 < 1.

Hali tarjima qilinmagan