Markov Transition Kernel

• $T_n(x|y)=P_n(X_{n+1}=x|X_n=y)$ for all $x,y\in S$
• Homogenous if $T_n(x|y)=T_{n^{\prime }}(x|y)$ 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
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