Module 1:Concepts of Random walks, Markov Chains, Markov Processes
Lecture 3:Markov Chains
Theorem 1.3 A state is recurrent iff
Proof of Theorem 1.3
Assume state is recurrent then we must havemust have, which is what we need to prove. Now pay close attention to the concept of generating function from where we see that, , and this is the generic form,from which we have (i) , , i.e., (ii) , (proof given above),would also imply , which would immediately prove that , as for (refer above prove). Now using the second proof which is: if and ,
is 
is 
, which is what we need to prove. Now pay close attention to the concept of generating function from where we see that, 
, 
and this is the generic form,from which we have (i) 
, 
, i.e., (ii) 
, 
(proof given above),would also imply 
, which would immediately prove that 
, as 
for 
(refer above prove). Now using the second proof which is: if 
and 
,
