I'm a new user and first of all congratulations, this forum is very useful, I'm finding out a lot of interesting answers, I hope I can contribute soon.
I've got a question about Markov chains.
Studying a manual I've found out the following theorem, related to one of the canonical representations of Markov chains:
Let be a sequence of i.i.d. random variables with values in a denumerable space .
Let a new sequence of random variable with values in a denumerable space , with a generic function ( a random variable on a denumerable set ).
If for all :
then is a Markov chain.
In other words, the previous hypothesis implies that:
The manual doesn't show the proof and I tried to prove it but I didn't succeed.
Could anybody help me obtaing the proof or links to other lecture notes with the solution?
Thanks in advance!