markov chain notation $X - Y - Z$

Question

In a markov chain, there is a random variable $X_k$ indexed by time $k$, which takes values in a finite set denoted by $\mathcal{X}$.

In reading some research papers, I encountered the notation $X - Y - Z$ as representing a Markov chain. Does this notation mean there is a random vector $V_k = (X_k, Y_k, Z_k)$, which takes values in a set $\mathcal{X} \times \mathcal{Y} \times \mathcal{Z}$?

I don't really know what the notation means, I am just guessing.

Answer 1

$X - Y - Z$ means that $X$ and $Z$ are conditionally independent, given $Y$

$$p_{X,Z|Y}(x,z|y) = p_{X|Y}(x|y)\, p_{Z|Y}(z|y)$$

Also equivalent to $$p_{X|Y,Z}(x|y,z) = p_{X|Y}(x|y)$$

or

$$p_{Z|Y,X}(z|y,x) = p_{Z|Y}(z|y)$$