A stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
A discrete-time Markov chain, also called a DTMC or Markov chain, (separate from a continuous-time Markov chain)is a state machine-like random process with the Markov property. In layman's terms, when the process chooses what the next step will be, its history has no impact on the choice.
Andrey Markov (or Markoff; Russian: Андре́й Андре́евич Ма́рков) produced the first results for Markov chains in 1906, though they were purely theoretical. Markov chains have been used for things ranging from natural language processing to Google's PageRank algorithm.
One more famous Markov chain is the random walk, where a point in space is chosen as an origin and takes "steps" in random directions, because the next state is dependent only on the current state, not on the history. Another famous example of a Markov chain is the casino game craps, where players throw die to determine the outcome -- and the next roll, of course, doesn't rely on the ones before, giving the the Markov property.
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