Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and continuous state space
Lecture 10:Application of Markov Chains
Definition
Consider are the random variables that denote the size of the 0th generation, 1st generation, etc respectively, Figure 3.1. Also assume that an individual in any generation produce number of off-springs and the probability be , . It is quite simple to note that . Then the sequence, , i.e., is the Galton Watson branching process.
In the Galton Watson branching process let us assume , where as per definition is the total number of progeny upto to the generation.
are the random variables that denote the size of the 0th generation, 1st generation, etc respectively, Figure 3.1. Also assume that an individual in any generation produce 
number of off-springs and the probability be 
, 
. It is quite simple to note that 
. Then the sequence, 
, i.e., 
is the 
, where as per definition 
is the total number of progeny upto to the 
generation.
if 
if 
if 
and 
