Markov chain


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Markov chain (a discrete stochastic process of Markov type) is a sequence of random events with a finite number of possible outcomes, in which the future depends on the current state, but does not depend on the past.

 

Markov chain, or as it is called, a Markov process, occupies a central place in the theory of random processes. The theory of stochastic processes is a science that studies the laws of random phenomena in the dynamics of their development.
This class of random processes was named after the Russian mathematician Andrey Markov (1856-1922). Markov is considered a pioneer of a whole class of stochastic processes with a discrete and continuous time component.

Processes occurring in the physical system, are called a Markov process, in case at any time the probability of any state of the system in the future depends only on the state of the system at the moment and does not depend on how the system came into such state.

A random events sequence called a Markov chain if each transition from one state to another does not depend on when and how the system arrived at the current state. The initial state can be set in advance or be accidental.

The principle of the Markov chain can be explained by the example of strings of words. For example, in the text of a sports reportage after the word “penalty” it is much more likely to meet the word “kick” rather than the word “battalion”.

A Markov chain is used as a method of prediction in a variety of areas: economic, social, political, financial, for the analysis and processing of text, and for other purposes. For example, the Markov chain is used in typing systems like T9.

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