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Definition
Discrete-Time Finite State Markov Chains
Markov Property
Given current state, the past doesn’t matter.
\[\begin{align} p_{ij}&=\mathbf{P}(X_{n+1}=j\,\lvert X_n=i)\\ &=\mathbf{P}(X_{n+1}=j\,\lvert X_n=i,X_{n-1},\ldots,X_0) \end{align}\]