Hello all,

I would be grateful if somebody could advise me or comment on a Markoc Chain question that I have. It is with regards to the state selection.

Say for example I recorded the velocity of a car every second for the length of a journey. Then I select velocity as the only state and compute the transitional probability matrix of moving from velocity to another.

Now say for instance that I compute the acceleration from the recorded velocity every second of that same journey. And this time I select 2 states acceleration and velocity. So I would have a matrix that looks like this

http://dl.dropbox.com/u/54057365/All/TPM.JPG

My question is, are these two examples the exact same because I calculated the acceleration directly from the recorded velocity? Or is there a difference? I have been told that one of the states is redundant but I'm not sure?

This image was taken from a paper, I can provide the paper if somebody would care read more about it.

Thank you for your help

Regards

John