Re: How Chapman-Kolmogorov implies Markov ??

On Feb 10, 9:58 am, "rayoha...@xxxxxxxxxxxx" <juanp...@xxxxxxxxx>
wrote:
<...>

ok, change the notation if you wish, but you don´t show (a proof) that
chapman-kolmogorov implies markov ...

I am beginning to think it doesn't. At least it doesn't if the
meaning of the relation which came on me in a flash is the correct
one: subject relation merely makes the unremarkable claim that,
starting in a state f_1 (state of the Markov chain realized at step
1), that the probability of ending in a particular f_3 (state of the
Markov chain at step 3), is obtained by summing a suitable expression
over all possible intermediate states f_2.

Hmm... well, clearly ... it isn't that clear after all. :-)

Isn't the way we write the thing out going to _imply_ the Markov
structure? Whether the Chapman-Kolmogorov equality implies a Markov
chain is a function of what you want to allow as the Chapman-
Kolmogorov equality -- since you could carry out the same operation
for a process missing some required property, then the answer is "no",
unless we refuse to label that operation "the Chapman-Kolmogorov
equality". It's all a trivial tautology, anyway you slice it, once
you disect the notation.

Most of math and science is like that. Sometimes it's a long
disection, I'll grant you.

.

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