Hi!

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!