Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and                 continuous state space
  Lecture 10:Application of Markov Chains
 

Extinction probability

Let us now try to find the ultimate extinction probability.
Assume:

Now we know that

So  iff

Thus  if  and it can also be shown that  if , i.e.,  if
Thus

Thus when  then  will be the smallest positive root of the equation .