Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Markov chain , named after Andrey Markov is a random process where all information about the future is contained in the present state (i.e. one does not need to examine the past to determine the future). To be more exact, the process has the Markov property, meaning that future states depend only on the present state , and are independent of past states . In other words, the description of the present state fully captures all the information that could influence the future evolution of the process. Being a stochastic process means that all state transitions are probabilistic (determined by random chance and thus unpredictable in detail, though likely predictable in its statistical properties).

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