\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
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In a Markov chain \((X_n)\), the probability \(P(X_{n+1} = j \mid X_n = i, X_{n-1} = i_{n-1}, \dots)\) depends only on:
The initial state \(X_0\).
The current state \(X_n\).
The entire history of states from \(X_0\) to \(X_n\).
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