Formal Definition
A Markov chain is a sequence of random variables X1, X2, X3, ... with the Markov property, namely that, given the present state, the future and past states are independent. Formally,
The possible values of Xi form a countable set S called the state space of the chain.
Markov chains are often described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other states.
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