# Markov Transition Kernel - $T_{n}(x|y) = P_{n}(X_{n+1}= x | X_{n}= y)$ for all $x,y \in S$ - Homogenous if $T_{n}(x|y) = T_{n'}(x|y)$ for all n,n' - First get a value from a random drow from $P_{X_{1}}$ - Then get the next from the distribution which is specified by the transition kernel -