ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4814 on D3348: Markov chain

Markov chain triple iff reverse is a Markov chain triple

Formulation 0

Let $X$, $Y$, and $Z$ each be a D202: Random variable.

Then the following statements are equivalent

(1)	$X \to Y \to Z$ is a D3348: Markov chain
(2)	$Z \to Y \to X$ is a D3348: Markov chain

Proofs

Proof 0

Let $X$, $Y$, and $Z$ each be a D202: Random variable.

Follows from the characterisation result R4811: Markov chain triple iff endpoints conditionally independent since the conditional independence relation is symmetric. $\square$