The Data Processing Inequality

Markovity

A Markov Chain is a random process that describes a sequence of possible events where the probability of each event depends only on the outcome of the previous event. Thus, we say that $X,Y,Z$ is a Markov chain in this order, denoted as:

$X\rightarrow Y\rightarrow Z$

(1)

If we can write:

$P\left(X=x,Y=y,Z=z\right)=P\left(Z=z\mid Y=y\right)\cdot P\left(Y=y\mid X=x\right)\cdot P\left(X=x\right)$

(2)

Or in a more compact form:

$P\left(x,y,z\right)=P\left(z\mid y\right)\cdot P\left(y\mid x\right)\cdot P\left(x\right)$

(3)