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I created a brief summary of definitions and theorems related to basic classification of Markov chain states. There is even a couple of diagrams that helped me learn some of the rules. Download, enjoy, and let me know what I can improve!
A Markov chain is a sequence of random variables (states) satisfying the Markov property: the probability of the current state depends only on the state that immediately preceded it. In other words, the past state and the future state are stochastically independent. How can we simulate such chains in Wolfram Mathematica?